Games, Mathematics

Games, Mathematics:Probability Puzzles Outrageous 9/18 (solved 9)

100px-nuvola_apps_atlantik

Incremental Update

Probability puzzle is available on google app store:

it comprises of 3 levels of difficulty:

Outrageous:

  1. Foxes multiplied by hounds divided by the total 5*7/12
    Answer: 5*7/12
  2. It’s every permutation of two different digits I used E (east) and N (north), were there is 7 E and 4 N which equals 330
    Answer: 330
  3. 1 minus all possible ways for the mouse to reach the trap multiplied by the ways to get from the trap to the cheese divided by 330 equals 1-6*21/330
    Answer: 1-6*21/330
  4. Ok, so this one is a little tricky, first you can see that train B will be there in 3 minutes no matter what happens with train A. So if Train A does not arrive in 3 minutes or less then the average is 1.5 minute wait time which occurs 2/5 of the time. Now if Train A does make it in the firs 3 minutes then the average wait time between both trains is 1 minute which occurs 3/5 of the time. So the equation is (1.5*2/5)+(1*3/5)
    Answer: (1.5*2/5)+(1*3/5)
  5. There us 13 positions possible to make a couple, 13 seats, with 5 men, and 8 women in a round table.
    Answer: 13*(8/13*5/12+5/13*8/12)
  6. Same as the top question except we lose possible chance to make a couple.
    Answer: 12*(8/13*5/12+5/13*8/12)
  7. There is no correlation, however since it’s those in college the high math or English skills allow you in without the other so it becomes -0.5
    Answer: -0.5
  8. Answer:
  9. This is almost exactly the same question as getting serious question 18. Not only can it be done the exact same way but it also uses the same number so it is the same answer (1/3)*(1/3)
    Answer: (1/3)*(1/3)
  10. Answer:
  11. This is another logic question, the answer is 1
    Answer: 1
  12. Answer:

 

That is the progress so far.

don’t forget to check the earlier levels: Getting serious

Thanks for Ralph for keep these answers coming.

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Games, Mathematics

Games, Mathematics:Probability Puzzles Getting serious 33/33 (solved 33)

100px-nuvola_apps_atlantik

Incremental Update

Earlier stage: Easy Peasy

Next stage: Outrageous

Probability puzzle is available on google app store:

it comprises of 3 levels of difficulty, this is the second one:

2- Getting serious:

  1. Well, you are tossing a dice, How many tosses to get a number larger than 4.
    Hint: [5,6]
    Answer: 3 tosses
  2. what is the probability that some of the people shares their birthday. (for more info: https://en.wikipedia.org/wiki/Birthday_problem (Very interesting, promise)
    Answer: 1-364*363/365^2
  3. what is smallest group size such that the probability of a common birthday is bigger than half.
    Answer: 23
  4. on average how many tosses does it take to get two heads in a row?
    Answer: 6
  5. someone selects a coin uniformly at random from the jar and tosses it. if it comes up heads, what is the probability the coin is fair?
    Answer: 1/3
  6. Babies are 0.51 boys, 0.49 girls.
    Answer: 3*(0.51^2)*0.49 = 0.3823
  7. the unpleasant disease problem, The trick here is to remember who is positive and who has the disease based on actual prevalence and population size
    Answer:148.5/(148.5 + 998.5)
  8. Each one of the 9 regular coins accounts for 1/8 possibilities of 3 heads. The two headed coin accounts for 8/8 possibilities.
    Answer:8/17
  9. The hint give you a big clue here on the formula to use, it’s 4/1+4/2+4/3+4/4
    Answer:4/1+4/2+4/3+4/4=8.3333
  10. basketball team, your skills are between 0 and 1, maximize your chance to join the team
    Answer: 3/5 = 0.6
  11. the shooting game
    Break the question up in to parts
    Chances of A killing B in the first round is 1/2 if this occurs there is a 2/3 chance that C wins and a 1/3 chance that A wins
    Chances of A missing B and B missing C is 1/8 in that case there is a 1/16 chance that A will die and a 1/16 chance that the new round starts with exactly the same odds of winning or losing as the previous round
    Chance of A missing B and B killing C 3/8 in that case A has a 3/16 + 3/(16*8) + 3/(16*8*8) + 3/(16*8*8*8) + …
    In the end if you add that all up you will get that A has about a 40.634% chance to win the duel (interestingly enough B has the worst chance to win the duel despite being the best shot and if A intentionally misses his first shot then his chances to win sky rocket)
    Answer: 128/315 or 0.40634 or 40.634%
  12. As send by Ralph: “You basically take the amount of two step jumps and make the combinations out of it, we know the minimum two step jumps is 0 and the max is 4 so:
    0 two step jumps = 1 combination
    1 two step jumps = 8 combination
    2 two step jumps = (6+5+4+3+2+1) = 21 combination
    3 two step jumps = (4+3+2+1)+(3+2+1)+(2+1)+(1) = 20 combination
    4 two step jumps = 5 combination
    1+8+21+20+5=55”
    Answer: 55
  13. Answer: 89
  14. The binary string
    I started with small strings and looked for a pattern,
    1/4 consecutive 1s
    3/8 consecutive 1s
    8/16 consecutive 1s
    The denomination is easy just multiply the previous denominator by 2. But the numerator was harder so after trying a few that failed the patter I noticed that you add the previous numerator to the sum of it’s combined previous numerator and denominator so the next string is
    (8+3+8)/32=19/32
    Then the next string is
    (19+8+16)/64=43/64
    Then the next string is
    (43+19+32)/128=94/128
    then the final string is
    (94+43+64)/256=201/256
    Answer: 201/256
  15. Its easier if you start backwards, we know there are 3 rounds, so in round three your expected to win (1+2+3+4+5+6)/6=3.5
    So in round 2 you should either stop at 4,5, or 6; otherwise just go to round 3. So in round 2 your expected to win (4+5+6)/3=5 at a 50% chance or 3.5 at a 50% chance. So in round 1 you should either stop at 5 or 6 otherwise just go to round 2. Therefore 5.5/3+5/3+3.5/3 or 14/3 is the expected payoff or value of the game.
    Answer:14/3
  16. The hint gave me a clue that it’s always the same, so I assumed what if there where two chairs and two passengers, then there is a 50% chance that the first passenger sat in his own chair. What if there is 3 seats and 3 passengers then there is a 2/3 chance that the first passenger sat in a seat that isn’t his and (1/2)*(1/3)=1/6 chance for the second passenger also meaning the last passenger will have a 50-50 chance of someone sitting in his chair. It seems to be true that if seats are more than 1 and passengers = seats then under those conditions the answer is always 1/2.
    Answer: 1/2
  17. Ralph: “Here is the answer is shows, 100*(1-0.19^0.5)/0.9. I had to look this formula up, but I used (100/9)*(10-4.359) note I probably had to be more significant than 5.359, it’s supposed to be the square root of 19, but I don’t know how to do that on android keyboard”
    Answer: 100*(1-0.19^0.5)/0.9
  18. The biologist and the bacteria
    This one takes a bit of math to solve. First let X equal the chance that a single bacteria will eventually die out (This is not 0.25 because it is not the chance it will die out in the next period).
    X=0.25*(1+X^2+X^2+X^2)
    X=0.25+0.75X^2
    4X=1+3X^2
    3X^2-4X+1=0
    Factors to
    (X-1)*(3X-1)=0
    So X is either 1 or 1/3.
    1 is impossible because that is a 100% chance to die out so each bacteria has a 1/3 chance to die out meaning the answer is (1/3)*(1/3)
    Answer:(1/3)*(1/3)
  19. You get this by factoring 1000 by 7, 11, and 13 and then remove any repeats
    Answer:280/1000
  20. The first day is automatically a block, the rest of the equation is a 0.8 chance (if it’s cloudy or sunny) of a 0.6 chance of a new block plus a 0.2 chance (rainy) of a 0.8 probability of a new block over the next 9 days so the equation is 1+9*(0.8*0.6+0.2*0.8)
    Answer: 1+9*0.8^2
  21. Answer: 1+9*0.7 however I solved it the same way I did question 20, my formula was 1+9*(0.5*0.5+0.25*0.75+0.25*1.05)
  22. It’s an equation, in which 2 fractions multiply together to get 1/2 while following the marbles rule
    In this case (3/4)*(2/3).
    Answer: 6
  23. Of those with 0.9 or more math ability, 95% are in university. Of the general population 50% are in university. 0.9 math ability is 10% of the population. So 0.95*0.1/0.5 or 19%
    Answer:0.95*0.1/0.5
  24. Answer:0.49
  25. Answer: 2*0.51*0.49^2 I can’t remember exactly how i got this. honestly this one gave me a lot of trouble and I think I lucked in to it, I still don’t understand why the answer isn’t 0.49*0.51
  26. Answer: I just used the slope formula for this, so (80-20)/(100-0)
  27. what is the expected length in meters of he longer piece?
    Answer: 3/4
  28. It’s logic, read the question again it’s asking how much time the clock will spend at 3 from now to infinity
    Answer: 1/12
  29. Answer: I looked up the Markov process to finally get this, I can’t remember what my equation looked like but this is the answer 252*0.5^10
  30. Answer: This one is just logic, if you read carefully you should get it, the answer is 0.6
  31. Answer: 1 – e^(-1) I know that wasn’t my formula, I looked up the formula bootstrapping and it showed two different formulas, one for small sample and one for infinitely large sample, I don’t think I had to plug in any numbers at all from what I recall the answer is just that formula
  32. Answer: 4/10, I wish it saved my original formula because it a lot bigger, from what I recall I did different variations of votes where C must get votes 1 and 2, T can only get one or zero votes when 3 votes are counted, can have two or less when vote 5 is counted, and can not have all 3 of his votes until at least the 7th vote is counted, I then divided that number by every possible permutation of the counted votes
  33. Answer: This is another logic question, the answer is 0.6

 

Thanks to Ralph and Manuel for contributing to this solution post.

Computer, Games

Computer, Games: Hacked app solutions Levels 7-10 {Finale} (Copied)

Level Seven: Nuclear Plant

First Episode

Second episode

Stage One:

foreach var_a in input {
input.push(var_a + 1).remove(0);
}
return input;

OR

var_b = [];
foreach var_a in input {
var_b.push(var_a + 1);
}
return var_b;

Stage two:

function f1: var_a {
return var_a > -1;
}
return input.map(f1);

OR

input.map(function var_a -> (var_a > -1));

OR

var_b = [];
foreach var_a in input {
var_b.push(var_a > -1);
}

Stage three:

function f1: var_a {
return var_a[0] + 1 * var_a[1] + 1;
}
foreach var_a in input {
if var_b == 0 || var_b > f1(var_a) {
var_c = var_a;
var_b = f1(var_a);
}
}
return var_c;


Level Eight: Killer Robot

Stage One:

function f1: var_a {
foreach var_b in var_a {
var_c = var_c * 10 + var_b;
}
return var_c;
}
var_b = f1(input[0]) + f1(input[1]);
var_a = [];
var_c = var_b / 10;
if var_c > 0 {
var_a.push(var_c);
}
var_a.push(mod(var_b, 10));

Stage two:

var_a = [];
foreach var_b in input {
if var_b == “(” || var_b == “[” {
var_a.push(var_b);
}
else {
if var_a.length == 0 {
return false;
}
var_c = var_a.pop;
if var_c == “(” && var_b != “)” {
return false;
}
if var_c == “[” && var_b != “]” {
return false;
}
}
}
return var_a.length == 0;


Level Nine: Skynet

Stage One:

function f1: var_a, var_b {
if var_b.is_list {
while var_b.length > 0 {
f1(var_a, var_b.remove(0));
}
}
else {
var_a.push(var_b);
}
return var_a;
}
f1([], input);


Level Ten: Retirement

Stage One:

draw(input[0],input[1]);


That’s all, Folks.

Thanks to Mr. Andrew.

Computer, Games

Computer, Games: Hacked app solutions Levels 4-6 (Copied)

Level Four: Cheatcode

First Episode

Third and final episode

Stage One:

while var_a < input.length {
var_b = var_a + 1;
while var_b < input.length {
if input[var_b] < input [var_a] {
var_c = input[var_b];
input[var_b] = input[var_a];
input[var_a] = var_c;
}
var_b++;
}
var_a++;
}
return input;

Stage Two:

var_a = [];
foreach var_b in input.sort {
while var_b != var_c {
var_a.push(var_c++);
}
var_c++;
}
return var_a;

Stage Three:

var_a = “”;
foreach var_b in input {
if var_a != var_b.sort && var_a != “” {
return false;
}
var_a = var_b;
}
return true;


Level Five: Corrupted

Stage one:

var_a = input.length -1;
while var_a > -1 {
var_b = var_b + input[var_a] * pow(2, input.length – var_a – 1);
var_a–;
}
return var_b;

Stage two:

if input == 1 {
return false;
}
var_a = 2;
while var_a < input {
if mod(input, var_a) == 0 {
return false;
}
var_a++;
}
return true;

Stage three:

while var_a < input.length – 1 { if input[var_a] > input[var + 1] {
return false;
}
var_a++;
}
return true;


Level Six: Cyber Attack

Stage One:

while var_a < input.length {
var_b = var_a;
while var_b != input[var_a] {
input.insert(var_a++, var_b++);
}
return input;
}

OR

var_a = [];
var_b = input.pop + 1;
while var_c < var_b {
var_a.push(var_c);
var_c++;
}
return var_a;

Stage two:

if input[0] == “)” {
return false;
}
foreach var_a in input {
if var_a == “(” {
var_b++;
}
else {
var_b–;
}
}
return var_b == 0;

Stage three:

return input.push(input.remove(0));

Games

Games: Alchemy Fusion 2

Air, Earth, Fire and Water
A
1 Acid = Sulfur + Water
2 Africa = Continent + Sand
3 Air
4 Aircraft carrier = Fighter + Ship
5 Airplane = Car + Sky
6 Airship = Balloon + Hydrogen
7 Alarm clock = Bell + Watch
8 Album = Camera + Book
9 Alcohol = Fruit + Sugar
10 Algae = Life + Ocean
11 Alien = Life + Stars
12 Aluminum = Air + Metal
13 Amber = Resin + Time
14 Ambulance = Car + Hospital
15 Anchor = Chain + Ship
16 Angel = Life + Light
17 Animal = Earth + Lizard
18 Ant = Acid + Animal
19 Antarctica = Ice + Continent
20 Antibiotic = Mold + Scientist
21 Anvil = Hammer + Metal
22 Apple = Fruit + Tree
23 Apple pie = Apple + Dough
24 Aquarium = Fish + Glass
25 Arable = Earth + Tools
26 Archipelago = Island + Island
27 Ark = Boat + Animal
28 Armchair = Chair + Pillow
29 Armor = Knight + Uniform
30 Army = Soldier + Soldier
31 Arrow = Bow + Feather
32 Ash = Cigarette + Fire
33 Ashtray = Ash + Glass
34 Asia = Continent + Porcelain
35 Astronaut = Man + Moon
36 Atlas = Book + Road
37 ATM = Bank+ Money
38 Atom bomb = Uranium + Weapon
39 Aurora-borealis = Rainbow + Planet
40 Australia = Continent + County
41 Avalanche = Mountains + Snow
42 Axe = Sword + Tools
B
43 Backpack = Book + Bag
44 Bacon = Pig + Fire
45 Bacteria = Swamp + Life
46 Bag = Box + Canvas
47 Bagpipes = Bag + Flute
48 Bakery = House + Break
49 Ball = Wheel + Canvas
50 Balloon = Canvas + Fire
51 Ball-pen = Ink + Feather
52 Bamboo = Asia + Tree
53 Banana = Monkey + Fruit
54 Bandage = Blood + Canvas
55 Bank = House + Money
56 Bar = Alcohol + House
57 Barrel = Board + Rim
58 Bat = Animal + Vampire
59 Batman = Bat + Hero
60 Bat-mobile = Batman + Car
61 Beach = Sand + Sea
62 Bear = Animal + Forest
63 Beaver = Animal + Dam
64 Bed = Pillow + Wood
65 Bee = Beetle + Flower
66 Beehive = Bee + Wood
67 Beer = Alcohol + Can
68 Beet = Sugar + Seeds
69 Beetle = Bug + Earth
70 Bell=Drum+metal
71 Bench = Park + Wood
72 Bicycle = Wheel + Wheel
73 Bills = Money + Paper
74 Bird = Egg + Sky
75 Black Hole = Sun + Time
76 Blanket = Carpet + Fur
77 Blizzard = Snow + Wind
78 Blood = Needle + Man
79 Blueberries = Fruit + Grass
80 Boar = Pig + Forest
81 Board (wood) = Saw + Wood
82 Board = Chess + Board (wood)
83 Boat = Trolley + Sea
84 Bomb = Metal + Gunpowder
85 Bone = Dog + Meat
86 Bbonsai = Tree + Pot
87 Book = Paper + Man
88 Boots = Sidewalk + Skin
89 Bottle= Plastic + Glassful
90 Bouquet = Flower + Flower
91 Bow = Hunter + Wood
92 Box = Cardboard + Cardboard
93 Bread = Furnace + Dough
94 Brick = Clay + Fire
95 Bridge = Road + River
96 Broom = Dust + Tools
97 Bug = Earth + Plankton
98 Bulb = Glass + Electricity
99 Bullet = Firearm + Arrow
100 Bunker = House + Earth
101 Butterfly = Air + Bug
C
102 Cable = Rope + Electricity
103 Cactus = Desert + Tree
104 Cage = Aquarium + Metal
105 Calendar = Paper + Time
106 Camel = Animal + Desert
107 Camera = Drawing + Microprocessor
108 Camera Lens = Camera + Lens
109 Campfire = Grill + Wood
110 Can = Aluminum + Glassful
111 Canal = Road + Ship
112 Canary = Mine + Bird
113 Candle = Wax + Fire
114 Candlestick = Candle + Silver
115 Candy = Caramel + Stone
116 Candyfloss = Sugar + Cotton
117 Canned = Metal + Metal
118 Cannon==Pipe+gunpowder
119 Canvas = Cotton + Tools
120 Caoutchouc = Tree + Juice
121 Cape = Hero + Clothes
122 Car = Combustion engine + Wheel
123 Caramel = Sugar + Fire
124 Carbon dioxide = Man + Air
125 Cardboard = Paper + Paper
126 Cards = Gambling + Paper
127 Carousel=Wheel+toys
128 Carpet = Canvas + Drawing
129 Carriage = Horse + Trolley
130 Carrot=Vegetables+Arable
131 Case = Skin + Clothes
132 Castaway = Island + Man
133 Castle = Stone + Knight
134 Cat = Animal + Milk
135 catapult=castle+slingshot
136 Cave = Dragon + Mountains
137 Caveman = Man + Cave
138 Caviar = Fish + Egg
139 C.D. = Book + Laser
140 Cement = Dust + Fire
141 Cemetery = Grave + Grave
142 Centaur = Animal + Man
143 Ceramics = Clay + Man
144 Chain = Rope + Metal
145 Chair = Bench + House
146 Chameleon=Lizard+Rainbow
147 Champagne = Wine + Sparkling Water
148 Charlock = Seeds + Sand
149 Cheese = Milk + Fire
150 Chess=Knight+castle
151 Chess Piece=Chess+Statue
152 Chest=Case+wood
153 Chisel=Statue+tools
154 Chocolate = Cocoa + Sugar
155 Cigar = Tobacco + Tobacco
156 Cigarette = Tobacco + Paper
157 Cinema = House + Film
158 Circus = Elephant + Tent
159 Claws = Animal + Weapon
160 Clay = Swamp + Sand
161 Cliff = Mountains + Sea
162 Clip = Laundry + Wood
163 Clothes = Canvas + Man
164 Clouds = Air + Steam
165 Clown = Circus+man
166 Coal = Wood + Fire
167 Cocoa = The Caribbean + Seeds
168 Coconut = Palm + Seeds
169 Coffee=Seeds+Tea
170 Coffin = Man + Death
171 Combustion engine = Steam engine + Petroleum
172 Comet = Meteorite + Ice
173 Comics = Book + Hero
174 Compost = Hay + Time
175 Computer = Microprocessor + Tools
176 Concrete = Cement + Sand
177 Confetti = Scissors + Paper
178 Conflagration = Matches + House
179 Continent = Earth + Mountains
180 Cookies = Chocolate + Dough
181 Cork = Wood + Bottle
182 Cornflakes = Grain + Milk
183 Cotton = Feather + Farm
184 Country = Town + Town
185 Court = Ball + Grass
186 Cow = Animal + Farm
187 Cowboy = Man + Horse
188 Crayons = Pencil + Rainbow
189 Creeper = Jungle + Rope
190 Crocodile = Lizard + River
191 Crop circles = UFO + Grain
192 Crown = Hat + Gold
193 Crumbs = Bird + Bread
194 Crystals = Quartz + Mountains
195 Cup = Glassful + Porcelain
196 Cutlery = Silver + Tools
D
197 Dactyl = Palm + Fruit
198 Dam = Concrete + River
199 Day=Earth+Light
200 Death = Time + Man
201 Demon = Lava + Life
202 Deodorant=Perfume+Can
203 Desert = Sand + Sand
204 Dew=Grass+Fog
205 Diamond = Coal + Time
206 Diet = Man + Yogurt
207 Dinosaur = Animal + Fossil
208 Diver = Man + Ocean
209 DNA = Life + Brick
210 Doctor = Hospital + Scientist
211 Dog = Wolf + Man
212 Dolphin = Animal + Fish
213 Door=Padlock+House
214 Dough = Flour + Water
215 Dragon = Fire + Lizard
216 Dragonfly = Fly + Lake
217 Drawing = Crayons + Paper
218 Dream = Man + Sand
219 Drink=Alcohol+Juice
220 Drum = Canvas + Ceramics
221 Dry ice= ice + carbon dioxide
222 Duck = Bird + Water
223 Dunes = Sand + Mountains
224 Dust = Earth + Wind
E
225 E-mail = Latter + Computer
226 Eagle = Bird + Mountains
227 Earth
228 Earthquake = Volcano + Energy
229 Earthworm=Bug+Rope
230 Ebook = Book + Computer
231 Eclipse = Earth + Moon
232 Eel = Snake + Electricity
233 Egg = Stone + Life
234 Eiffel tower = Metal + Skyscraper
235 Electricity = Metal + Energy
236 Elephant = Animal + Fang
237 Energy = Fire + Fire
238 Envelope= Letter + Paper
239 Explosion=fire+gunpowder
F
240 Factory = House + Tools
241 Fan = Wind + Paper
242 Fang = Animal + Bone
243 Farm = Arable + Man
244 Fashion = Time + Clothes
245 Fat = Oil + Meat
246 Feather = Bird + Hunter
247 Fence = Wood + Hedge
248 Fern = Moss + Swamp
249 Ferry = Ship + Car
250 Fiber = Rope + Glass
251 Fighter = Airplane + Firearm
252 Filings = Metal + Saw
253 Film = Television + Spider-man
254 Fins = Man + Fish
255 Fire
256 Firearm = Gunpowder + Weapon
257 firefighter=Man+fire
258 Firefly = Fly + Light
259 Fireworks = Asia + Gunpowder
260 Fish = Animal + Sea
261 Fisherman = Fish + Hunter
262 Fishing Rod = Bamboo + Tools
263 Flag = Canvas + Country
264 Flamethrower = Firearm + Fire
265 Fleet = Ship + Ship
266 Flood = Rain + Rain
267 Floor=House+board(wood)
268 Flour = Quern + Grain
269 Flower = Water + Seeds
270 Flute=Wind+Pipe
271 Fly = Bug + Compost
272 Foam = Soap + Water
273 Fog = Steam + Swamp
274 Forest = Tree + Tree
275 Forge = Anvil + House
276 Fossil = Animal + Time
277 Fox = Animal + Fur
278 Frame = Wood + Painting
279 French fries = Potato + Oil
280 Frog = Swamp + Lizard
281 Frosting = Sugar + Water
282 Fruit = Farm + Tree
283 Fur = Animal + Hunter
284 Furnace = Brick + Wood
285 Furniture = Screw + Wood
286 Fusion = Hydrogen + Hydrogen
G
287 Galaxy = Solar system + Solar system
288 Gale = Wind + Sea
289 Gambling = Alcohol + Money
290 Generator = Electricity + Combustion engine
291 Genie=Bottle+Ghost
292 Geyser = Earth + Steam
293 Ghost = Death + Energy
294 Giraffe = Animal + Tree
295 Glacier=Ice+wall
296 Glass = Fire + Sand
297 Glasses = Lens + Metal
298 Glassful = Glass + Man
299 Goat= mountains + animal
300 Godzilla=Lizard+radiation
301 Gold = Mine + Tools
302 Golem = Clay + Life
303 Gondola = Boat + Venice
304 Gong = Bell + Asia
305 G.P.S. = Computer + Road
306 Graffiti = Drawing + Wall
307 Grain = Arable + Seeds
308 Granary = Grain + Ceramics
309 Grape = Creeper + Fruit
310 Grass = Algae + Earth
311 Grave = Coffin + Earth
312 Greenhouse = House + Seeds
313 Grill = Coal + Metal
314 Guitar = Strings + Wood
315 Gunpowder = Coal + Sulfur
H
316 Hail = Ice + Rain
317 Hair = Fur + Man
318 Ham=Meat+smoke
319 Hammer=Wood+stone
320 Hamster = Animal + Cage
321 Hang-glider = Parachute + Airplane
322 Hangings = Windows + Canvas
323 Hat = Clothes + Straw
324 Hay = Grass + Sun
325 Hedge = Wall + Tree
326 Hedgehog = Animal + Needle
327 Helicopter = Combustion engine + Propeller
328 Helmet = Soldier + Hat
329 Hen = Bird + Egg
330 Herbs = Grass + Life
331 Hero = Dragon + Knight
332 Heron=Swamp+Bird
333 Hippo=swamp+animal
334 Honey = Beehive + Man
335 Horizon=earth+sky
336 Horse = Animal + Knight
337 Horseshoe = Horse + Metal
338 Hospital = Medication + House
339 Hourglass = Glass + Sand
340 House = Brick + Man
341 House For The Birds = Bird + House
342 Hovercraft = Ship + Air
343 Hulk = Hero + Radiation
344 Hummingbird = Bird + Flower
345 Hunter = Man + Weapon
346 Hurricane = Wind + Ocean
347 Hut = House + Stone
348 Hydrogen = Electricity + Water
I
349 Icarus = Feather + Sun
350 Ice = Glass + Water
351 Ice Cream = Ice + Milk
352 Ice sculpture=Statue+ice
353 Iceberg = Ice + Mountains
354 Igloo = House + Snow
355 Indonesia=archipelago+country
356 Infusion = Herbs + Water
357 Ink = Soot + Water
358 Internet = Computer + Net
359 Iron-man = Hero + Metal
360 Island = Sea + Volcano
J
361 Japan = Asia + archipelago
362 Jedi = Knight + Light saber
363 Jewelry = Gold + Silver
364 Juice = Fruit + Glassful
365 Jungle = Forest + Rain
K
366 Kangaroo = Animal + Australia
367 Killer = Death + Knight
368 Kimono = Clothes + Asia
369 King = Man + Castle
370 King Kong = Monkey + Skyscraper
371 Kite = Paper + Wood
372 Knife = Tools + Bread
373 Knight = Man + Sword
374 Knights Tournament = Knight + Knight
375 Koala = Bear + Australia
L
376 Laboratory = House + Scientist
377 Labyrinth = Castle + Hedge
378 Ladder= Rope + Wood
379 Lake = Water + Water
380 Lamp = Glass + Petroleum
381 Lantern = Lamp + Metal
382 Las Vegas = Desert + Town
383 Laser = Energy + Light
384 Lasso = Cowboy + Rope
385 Laundry= Clothes + Washing Machine
386 Lava = Earth + Fire
387 Leaf = Tree + Sun
388 LED=Bulb+Fiber
389 Leech = Vampire + Bug
390 Lemon=fruit+vitamins
391 lemonade = Lemon + Sparkling Water
392 Lens = Diamond + Glass
393 Leprechaun = Gold + Rainbow
394 Letter = Paper + Ink
395 Lettuce = Vegetables + Leaf
396 Library = Book + House
397 Life = Energy + Swamp
398 Light = Bulb + Electricity
399 Lighter = Matches + Metal
400 Lighthouse = Lantern + Sea
401 Lightning = Sky + Energy
402 Light saber = Sword + Light
403 Lily = Flower + Lake
404 Lion = Cat + Desert
405 Lizard = Egg + Earth
406 Locomotive = Trolley + Steam engine
407 Lollipop = Candy + Wood
408 Lunette = Lens + Lens
M
409 Magnet= Stone + Metal
410 Man = Golem + Life
411 Manga=Japan+comics
412 Manhole = Sidewalk + Steam
413 Mantis = Aquarium + Bug
414 Map = Paper + Road
415 Marble = Stone + Glass
416 Mars = Plant + Rust
417 Matches = Wood + Sulfur
418 Mayonnaise=oil+egg
419 Meadow = Grass + Grass
420 Meat = Electricity + Pig
421 Medal = Soldier + Metal
422 Medication = Herbs + Scientist
423 Metal = Fire + Stone
424 Meteorite = Stone + Solar system
425 Microprocessor = Electricity + Metal
426 Microscope = Bacteria + Lens
427 Milk = Cow + Grass
428 Mine = Mountains + Man
429 Minotaur = Man + Cow
430 Mirror = Canvas + Metal
431 Mixer = Knife + Electricity
432 Moat = Castle + River
433 Mold = Bread + Dust
434 Mole = Animal + Earth
435 Money = Factory + Gold
436 Monkey = Animal + Jungle
437 Moon = Sun + Ice
438 Mosaic = Drawing + Stone
439 Mosquito = Blood + Fly
440 Moss = Algae + Swamp
441 Moth = Butterfly + Fire
442 Motor-cycle = Bicycle + Combustion engine
443 Mountains = Earth + Earth
444 Mouse = Animal + Cheese
445 Mower = Combustion engine + Scythe
446 Mud = Dust + Water
447 Mummy = Bandage + Zombies
448 Museum = Painting + Statue
449 Mushroom = Forest + Grass
450 Music = Guitar + Man
451 Mustard = Charlock + Pressure
N
452 Necklace = Pearl + Rope
453 Nectar=Flower+butterfly
454 Needle = Cactus + Metal
455 Nest = Bird + Hay
456 Net = Rope + Rope
457 New York = Town + Statue
458 Newspaper = Camera + Paper
459 Night + Stars + Planet
460 Ninja = Samurai + Shadow
461 Nugget = Gold + Stone
O
462 Oasis = Desert + Water
463 Ocean = Water + Sea
464 Oil = Sunflower + Tools
465 Omelet = Egg + Fire
466 Opal = Stone + Rainbow
467 Orchard = Apple + Tree
468 Orchid = Flower + Jungle
469 Origami = Bird + Paper
470 Owl = Bird + Night
471 Oxygen = Tree + Carbon dioxide
P
472 Padlock = Chain + Chain
473 Painting = Crayons + Canvas
474 Palm = Island + Tree
475 Panda = Bamboo + Bear
476 Paneling = Board + Wall
477 Paper = Reed + Tools
478 Paper Airplane = Airplane + Paper
479 Paperclip = Clip + Metal
480 Paprika = Vegetables + Spices
481 Parachute = Canvas + Air
482 Paris = Eiffel Tower + Town
483 Park = Forest + Town
484 parrot = Jungle + Bird
485 Passport = Country + Paper
486 Pasta = Dough + Rope
487 Pavement = Road + Stone
488 Peacock= Bird + Rainbow
489 Pearl = Diver + Ocean
490 Pegasus = Horse + Steam
491 Pencil = Coal + Wood
492 Penguin = Bird + Ice
493 Perfume = Alcohol + Flower
494 Petroleum = Tree + Swamp
495 Pharaoh = King + Pyramid
496 Phoenix = Bird + Fire
497 Pig = Animal + Mud
498 Pigeon = Bird + Letter
499 Piggy bank = Pig + Money
500 Pillow = Canvas + Feather
501 Pineapple = Fruit + Arable
502 Pinocchio = Life + Wood
503 Pipe (smoking) = Tobacco + Wood
504 Pipe = Metal + Tunnel
505 Piranha = Fish + Meat
506 Pirates = Ship + Weapon
507 Pitchfork = Tools + Hay
508 Pizza = Cheese + Dough
509 Planet = Continent + Ocean
510 Plankton = Bacteria + Ocean
511 Plasma = Energy + Fire
512 Plastic = Metal + Petroleum
513 Plasticine = Clay + Crayons
514 Plume = Feather + Hat
515 Poison = Killer + Water
516 Polar Bear = Bear + Ice
517 Pompeii = Town + Lava
518 Pool = House + Water
519 Popcorn = Seeds + Fire
520 Porcelain = Clay + Quartz
521 Port = Ship + Beach
522 Postage Stamp = Envelope + Drawing
523 Pot = Ceramics + Flower
524 Pot (cooking) = Ceramics + Metal
525 Potato = Farm + Root
526 Power station = Dam + River
527 Pressure = Earth + Steam
528 Printing house = Book + Factory
529 Prison = Cage + House
530 Propeller = Fan + Wood
531 Pterodactyl=Bird+dinosaur
532 Pumice = Stone + Air
533 Puppet = Man + Straw
534 Puzzle = Scissors + Drawing
535 Pyramid = Desert + Skyscraper
Q
536 Quartz = Sand + Scientist
537 Quern = Wheel + Stone
R
538 Rabbit = Animal + Carrot
539 Radar = Air + Radio waves
540 Radiation = Radio waves + Radio waves
541 Radio waves = Electricity + Waves
542 Railroad tracks = Metal + Road
543 Rain = Sky + Water
544 Rainbow = Rain + Light
545 Reed = Grass + Lake
546 Reel = Wheel + Spindle
547 Refrigerator = Ice + House
548 Resin = Spruce + Juice
549 Ribs = Grill + Pig
550 Rice = Asia + Grain
551 Rim = Wheel + Metal
552 Ring = Diamond + Gold
553 Rink = Ice + Lake
554 River = Rain + Mountains
555 Road = Car + Earth
556 Roast = Fire + Meat
557 Robot = Computer + Man
558 Root = Earth + Tree
559 Rope = Yarn + Yarn
560 Rose = Flower + Needle
561 Rubber = Sulfur + Caoutchouc
562 Ruby = Diamond + Fire
563 Rum = Alcohol + Pirates
564 Rust = Metal + Water
S
565 Safe = Bank + Metal
566 Sail = Canvas + Ship
567 Sailing ship = Boat + Sail
568 Salad = Vegetables + Vegetables
569 Salmon=Fish+River
570 Salt = Sea + Sun
571 Samurai = Asia + Knight
572 Sand = Wind + Stone
573 Sandcastle = Castle + Sand
574 Sandpaper = Paper + Sand
575 Sandstorm = Sand + Wind
576 Sandwich = Meat + Bread
577 Satellite = Moon + Radio waves
578 Saturn = Rim + Planet
579 Sauna = House + Steam
580 Saw = Tools + Chisel
581 Scarab = Beetle + Gold
582 Scarecrow = Bird + Puppet
583 Scientist = Man + Library
584 Scissors = Metal + Paper
585 Scorpion = Beetle + Gold
586 Screw = Metal + Whirlpool
587 Screwdriver = Tools + Screw
588 Scythe = Grass + Scissors
589 Sea = Lake + Water
590 Sea Serpent = Dragon + Sea
591 Seagull = Bird + Island
592 Seal = Animal + Circus
593 Seeds = Life + Sand
594 Shadow = Light + Wall
595 Shark = Piranha + Sea
596 Sheep = Animal + Wool
597 Shell = Plankton + Stone
598 Shelter = House + Wood
599 Shield = Sword + Wall
600 Ship = Boat + Metal
601 Shoal = Fish + Fish
602 Shuriken = Ninja + Weapon
603 Sidewalk = Road + Man
604 Silver = Gold + Mirror
605 Siren = Man + Dolphin
606 skateboard = board + Wheel
607 Skates = Skis + Rink
608 Skin = Cow + Tools
609 Skis = Wood + Snow
610 Sky = Air + Clouds
611 Skyscraper = Glass + House
612 Sleigh = Trolley + Snow
613 Slingshot = Rubber + Bow
614 Smoke = Air + Fire
615 Snail = Bug + Shell
616 Snake = Egg + Swamp
617 Snow = Ice + Sky
618 Snow Globe = Glass + Snow
619 Snowman = Man + Snow
620 Soap = Fat + Water
621 Solar Panel=Sun+electricity
622 Solar system = Sun + Planet
623 Soldier = Firearm + Man
624 Soot = Coal + Fire
625 Space Station = Astronaut + Satellite
626 Sparkling Water = Water + Carbon = dioxide
627 Speaker = Drum + Electricity
628 Sphinx = Pyramids + Statue
629 Spices = Seeds + Herbs
630 Spider = Animal + Net
631 Spiderman = Hero + Spider
632 Spindle = Needle + Wood
633 sponge = Pumice + Canvas
634 Spruce = Tree + Needle
635 Squid = Animal + Ink
636 Stable = House + Horse
637 Stain = Clothes + Mud
638 Stained glass = Window + Rainbow
639 Stamp = Letter + Wax
640 Stars = Sun + Galaxy
641 Statue = Man + Stone
642 Steam = Fire + Water
643 Steam engine = Clouds + Metal
644 Steamer = Clouds + Ship
645 Sticks = Asia + Cutlery
646 Stone = Lava + Water
647 Storm = Electricity + Sky
648 Straw = Grain + Tools
649 Strings = Metal + Yarn
650 Sugar = Reed + Water
651 Suit=uniform+Clothes
652 Sulfur = Bacteria + Swamp
653 Sun = Energy + Hydrogen
654 Sunflower = Flower + Sun
655 Sunglasses = Glasses + Sun
656 Superman = Hero + Steam
657 Surfing = Man + Waves
658 Sushi = Fish + Rice
659 Swamp = Earth + Water
660 Sweater = Wool + Clothes
661 Sword = Metal + Tools
T
662 Tale = Book + Castle
663 Tank = Car + Firearm
664 Target = Bow + Canvas
665 Tarzan = Man + Jungle
666 Tattoo = Man + Ink
667 Tea = Cup + Herbs
668 Telephone = Microprocessor + Radio waves
669 Telescope = Galaxy + Lunette
670 Television = Drawing + Radio waves
671 Tennis = Court + Net
672 Tent = Canvas + House
673 Tequila = Alcohol + Cactus
674 Termite = Bug + Wood
675 Terrarium = Aquarium + Lizard
676 The Caribbean = Pirates + Island
677 The green lantern = Hero + Lamp
678 Thief = Man + Gold
679 Thor = Hero + Tools
680 Ticket = Circus + Paper
681 Tides = Moon + Ocean
682 Tiger = Cat + Zoo
683 Time = Hourglass + Life
684 Tire = Rubber + Wheel
685 Titanic = Ship + Iceberg
686 Titanium + Aluminum + Metal
687 Toast = Bread + Fire
688 Tobacco = Alcohol + Leaf
689 Tools = Man + Metal
690 Tornado = Propeller + Wind
691 Tower = Castle + Skyscraper
692 Town = Village + Village
693 Toys = Car + Drawing
694 Tractor = Farm + Trolley
695 Transformer = Life + Car
696 Treasure = Gold + Pirates
697 treasury= castle+ gold
698 Tree = Earth + Seeds
699 Tree House = House + Tree
700 Trolley = Wheel + Tools
701 Trout = Lake + Fish
702 Tsunami = Water + Wall
703 Tuna = Can + Fish
704 Tunnel = Cave + Road
705 Turtle = Egg + Sand
U
706 UFO = Alien + Airplane
707 Umbrella = Man + Rain
708 Uniform = Clothes + Soldier
709 Universe = Galaxy + Galaxy
710 Uranium = Metal + Radiation
V
711 Vampire = Blood + Zombies
712 Vanilla = Flower + Sugar
713 Vase = Flower + Glass
714 Vegetables = Earth + Fruit
715 Venice = Town + Sea
716 Village = House + House
717 Vinegar = Alcohol + Oxygen
718 Vitamins=fruit+medication
719 Volcano = Mountains + Lava
720 Volleyball = Beach + Net
721 Vulture = Bird + Death
W
722 Wall = Brick + Brick
723 Wallet = Crocodile + Hunter
724 War=army+army
725 Wardrobe = Clothes + House
726 Washing Machine = Clothes + Soap
727 Watch = Hourglass + Quartz
728 Water
729 Waterfall = Mountains + River
730 Watermelon = Water + Fruit
731 Waves = Lake + Wind
732 Wax = Beehive + Tools
733 Weapon = Metal + Wood
734 Werewolf = Zombies + Silver
735 Whale = Fish + Plankton
736 Wheel = Tools + Wood
737 Whirlpool = Tornado + Sea
738 Wind = Air + Air
739 Windmill = Quern + Wind
740 Window = Door + Glass
741 Wine = Grape + Alcohol
742 Wolf = Animal + Werewolf
743 Wood = Tree + Tools
744 Woodpecker = Bird + Tree
745 Wool = Cotton + Animal
Y
746 Yarn = Cotton + Reel
747 Yogurt = Bacteria + Milk
Z
748 Zebra = Africa + Horse
749 Zombies = Death + Life
750 Zoo = Animal + Fence
Computer, Games

Computer, Games: Hacked app solutions Levels 1-3 (Copied)

Level one: The Hackpad

Second episode

Third and final episode

Stage One:

input + 1;

Stage Two:

input> 0;

Stage Three:

if input < 0 {
return -input;
}
return input;

Stage Four:

abs(input);


Level two: High School Hack

Stage One:

while var_a < input {
var_b = var_b + input;
var_a++;
}
return var_b;

Stage Two:

pow(input, 2);

Stage Three:

foreach var_a in input {
var_b++;
}
return var_b;

Stage Four:

var_a = [];
while var_b < input {
var_a.push(var_b);
var_b++;
}
return var_a;


Hacked App – level three: Jailbreak

Stage One:

foreach var_a in input {
if var_a > var_b {
var_b = var_a;
}
}
return var_b;

OR

while var_a < input.length { if input[var_a] > var_b {
var_b = input[var_a];
}
var_a++;
}
return var_b;

Stage two:

foreach var_a in input {
var_b = max(var_b, var_a);
}
return var_b;

OR

while var_a < input.length {
var_b = max(var_b, input[var_a]);
var_a++;
}
return var_b;

Stage three:

while input > 1 {
input = input – 2;
}
return input;

OR

if input / 2 * 2 == input {
return 0;
}
return 1;

Stage four:

foreach var_a in input {
if var_a != input.pop {
return false;
}
}
return true;

OR

while var_a < input.length {
if input[var_a] != input[input.length – 1 – var_a] {
return false;
}
var_a++;
}
return true;


 

Games, Mathematics

Games, Mathematics:Probability Puzzles Easy Peasy 32/32 (solved 32)

100px-nuvola_apps_atlantik

Later stage: Getting serious

Probability puzzle is available on google app store:

it comprises of 3 levels of difficulty, This is the first one:

  1. Easy Peasy:
    1. Julius Ceasar tosses two fair coins, probability of two heads?
      Hint: [h,h – h,t – t,t – t,h]
      Answer: 1/4
    2. six individual socks, 2 red,2 blue, 2 purple.
      probability of blindly picking a matching pair.
      Hint: [you already picked one of six, the rest are 5, one of which is matching the one you have]
      Answer: 1/5
    3. rolling a fair six-sided dice, probability of even number.
      Hint: [1,2,3,4,5,6]
      Answer: 3/6 = 1/2
    4. roll two fair independent six-sided dice, probability of getting 12 in total.
      Hint: [1,1-1,2-1,3,………6,6]
      Answer: 1/36
    5. boys’ birth probability 0.51, girls’ 0.49, the probability of getting 2 girls birth.
      Answer: 0.49^2=0.49*0.49
    6. in a perfectly shuffled deck of 52 cards, with 4 aces, what is the probability of drawing 2 aces.
      Hint: if you draw one card, the deck is less by one.
      Answer: (4/52)*(3/51)
    7. in 40 cards deck with 4 aces-yet not drawn- what is the probability of drawing only one ace in two draws.
      Hint: first pick is ace, 4/40 and second pick is not an ace 36/39, remember these are 2 draws
      Answer: 2*(4/40)*(36/39) = (36/40)*(4/39)+(4/40)*(36/39)
    8. a deck contains 4 suits, 13 cards each, the probability of drawing two cards of same suit.
      Hint: first draw doesn’t count, in the second draw the deck is 51 cards this time and 12 cards of the required suit.
      Answer: 12/51
    9. These weird monkeys favor 3 types of berries, red, yellow, blue.
      but not all monkeys created equally.
      the probability of a monkey favoring red to blue and yellow
      Hint: [RYB,RBY,BRY,BYR,YRB,YBR], the trick here is the monkey prefers red over blue, but you are not sure that she prefers yellow to red or blue.
      Answer: 4/6
    10. you have stolen from the king, he is feeling generous, you are a smart guy, maximize you chance of survival in his game, 100 marbles, 50 white and 50 black marbles, put them in 2 jars.
      Jars have 50-50 chance to b picked.
      Hint:
      Answer: (1/2)*(1)+(1/2)*(49/99) = (1/2)+(0.495)=0.747 (Good Luck)
    11. Alice and Bob found unfair coin of 72% heads to 28% tails, they agreed to a game Alice will toss twice, if it comes up Heads then Tails, she wins; If came up Tails then Heads, Bob wins; if came up Heads or Tails it is a draw. What is Bob’s probability of winning?
      Hint: Since the two consecutive coin tosses are independent, Pr[HT]=Pr[H]Pr[T], and Pr[TH]=Pr[T]Pr[H]. Does the winner depend on the bias Pr at all?(Note that the probability that someone wins in the first round does depend on the bias; but since the game is repeated until either HT or TH happens, it does not. For more, you may want to read about von Neumann’s trick; essentially, Alice and Bob have equal chances of winning, but the (expected) duration of the game will depend on the bias p=0.72))
      Copied from http://math.stackexchange.com/questions/1622474/what-is-the-probability-of-bob-winning-the-game
      Answer: 1/2
    12. boys’ birth probability 0.51, girls’ 0.49, researcher is interested to interview 50 families in which they are exactly 8 children.
      what is the probability that at least in one family the children will all be of the same gender?
      Hint:
      Answer: 1-(1-0.51^8-0.49^8)^50 = 0.3274
    13. Monty Hall game with 10 doors 9 goats and a car, if you switch what is your probability of winning the car?
      Hint: at first you picked a door of 1/10 chance of winning, when the 8 doors were eliminated, the remaining one door (the one you didn’t pick) its chance didn’t change still at 1/10, but you odds have changed from 1/10 to 9/10.
      Answer:9/10
    14. you roll 2 six-sided fair dices, the probability that the sum of outcome is 7.
      Hint: only 6 combination of dices can result of 7, the total outcomes are 36.
      Answer: 6/36
    15. 0.05 of population are gays, 0.95 are straight, Susie can guess with 90% accuracy if one is gay or straight, what is the possibility that one is gay?
      Hint:
      Answer: (0.05*0.9) + (0.95*0.1)
    16. the three dice puzzles,
      Hint:
      Answer: 4/9
    17. ancient Romans, [0,2], [2,10],[10,30],[30,70] and [70,90], what is the life expectancy of an ancient Roman, who was still alive at age of 30?
      Hint:
      Answer: 65 years
    18. a friend wants you to guess the amount of money he has, if yuo guess right the cash is yours, 50% chance he has 0$,  25% chance he has 1$,  24% chance he has 100$,  1% chance he has 1000$ what is the amount you should guess in order to maximize your experience?
      Hint:
      Answer: 100$
    19. two departments A and B, A has a 50-50 men-women ratio,  B has 0.1 men and 0.2 women.
      the overall acceptance in both departments are 0.3for men, and 0.25 for women.
      Answer: 1/6
    20. Answer:17/36
    21. Answer: 1-0.2
    22. to calculate the outcome of two daughters, from a couple who declared they have one daughter already, 0.49 girl birth, 0.51 boy birth.
      Answer: (0.49*0.49)/((0.49*0.51)+(0.49*0.49)+(0.51*0.49)) = 0.3245
    23. Answer:30/50
    24. Answer:0.4/(0.4+0.6*0.5)
    25. Answer: 0.75
    26. Answer:1/2
    27. Answer: 3*0.05*0.95^2
    28. 140/969 because it is a combination. 16/20 * 15/19 * 14/18 * 2/17 * 2/16 and then because this is a permutation, multiply by the 20 different ways to organize this with the same groups, and you get .1444788442 or 140/969
      Answer
      : 140/969
    29. Answer:1/26
    30. Answer:5!
    31. It asks for 2 layers of combinations because we care that there are groups of 4 but not who is in them. So our first round is 12C4 then we have to figure out 8 into groups of 4 so 8C4 and 4C4 =1 so we simply do 12C4 * 8C4 which is 34650
      Answer:34650
    32. Answer: 6! – 10*4!

Thanks to Jackson and Ralph, for contributing to this solution post.

Congratulations, We have made it through the first level…
Check out the next level : Getting serious