Category Archives: Puzzle

This category is for logic and math puzzles. Have some fun with logic and math. This is to put some fun into it.

Puzzle #195: Chocolate

Your sweetie loves chocolate. You bought your sweetie some chocolate: an assortment of 24 chocolates with six each of four flavours. “Oh, honey, you shouldn’t have.” Why not? Unfortunately, chocolate causes your sweetie to gain weight per the following table:

Flavour Weight Gain in Grams per Chocolate Eaten

Nougat 100
Honey 200
Solid Chocolate 900
Anthrax Ripple -200

Your sweetie selects four chocolates at random and eats them.

What is the probability of each of the following scenarios occurring (assuming no other factors that affect weight)?

Scenario 1: Your sweetie gains two or more kilograms.

Scenario 2: Your sweetie’s weight does not change.

Scenario 3: Your sweetie loses weight.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, March 1, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #194: Dog Fu

Last week’s dogs were rather incompetent. This week, the focus will be on Bowser, Spot, and Fifi who are three dogs very skilled at Dog Fu. There are certain Dog Fu maneuvers that involve teamwork, a pack if you will. This pack respects Fluffy highly, but there are other cats that need a whacking.

The Dog Fu maneuver of Cat Smearing requires three Dog Fu practitioners. As it is a very advanced technique, even Bowser, Spot, and Fifi have difficulty pulling it off. Bowser has a 70% chance of pulling off his part, Spot 85%, and Fifi 45%. All must succeed for the maneuver to succeed.

Two successful applications of Cat Smearing will thoroughly whack any cat. If the pack tries Cat Smearing three times against a cat, what is the probability that they will successfully whack their target? Answer to the nearest 0.1%.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 22, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #193: Kara-Ashi

Fluffy the cat is minding his own business walking down a walled alley when he is set upon by three dogs. There is no way out. He will have to fight. Fortunately, Fluffy is a master of kara-ashi (Japanese for “empty paw”). By the way, “karate” means “empty hand”. A favourite kara-ashi maneuver of Fluffy’s is Dog’s Nightmare where he spins on one hind leg and lashes out with the other three paws hitting up to three times.

When Fluffy uses Dog’s Nightmare, he has a 50% chance of hitting once, 40% twice, and 10% all three times. Miss totally? Please do not insult the master.

The dogs will panic and break if they are hit a total of six or more times. What is the probability that Fluffy will accomplish this in three or fewer uses of Dog’s Nightmare?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 15, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #192: More Temperatures

It is warming up, and one of the answers to this one is rather warmer. What is the value for x where 2x°F = x°C or where 2x°C = x°F?

There are two answers.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 8, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #191: Temperatures

Just a bit of chill outside, eh? As you may know, -40°C = -40°F. What is the value for x where x°C = -x°F or where x°F = -x°C?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 1, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #190: More Alphabet Sets

Each letter of the alphabet has been put into one of three sets.

Set 1: A, F, H, K, M, N, P, Q, R, T, X, Y
Set 2: B, D, O
Set 3: C, E, G, I, J, L, S, U, V, W, Z

What is the rule for which set a letter goes into?

Hint: The solution has to do with the shape of the letter. Depending on the exact shape of I that you consider, I might belong in set 1 instead.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 25, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #189: Yet More Marbles

You have some marbles, each of one colour of red, orange, yellow, green, blue, and violet.

The total number of marbles is not evenly divisible by 4.

At least three of the marble colours have the same number of marbles as letters in the colour name.

The number of blue marbles plus the number of violet marbles is not equal to the number of red marbles plus the number of yellow marbles.

You have fewer red than green marbles, fewer yellow than blue, more orange than blue, more green than violet.

The number of marbles of each colour is the same as that of another colour.

How marbles are there of each colour?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 11, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #188: 2, 0, 1, 7

Come up with arithmetic expressions that evaluate to the integers from 0 to 10 using only the digits in 2017 exactly once each and as many and as often as you need of the following: brackets, addition, subtraction, multiplication, division, unary negative (as in –2), factorial (0! = 1, 3! = 3 × 2 × 1 = 6), and simply grouping digits (as in 201 – 7).

It is possible to solve this with each expression having the digits in the order 2, 0, 1, and 7, but this is not a requirement.

Happy New Year.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 11, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #187: Exact Change

Squareland has coins in several denominations. We will concern ourselves with only the 4-, 9-, 16-, 25-, 36-, 49-bit coins. They used to have a 1-bit coin but no more. You want to give someone exactly 50 bits in coin. How many ways are there to do this?

Hint: You could just start iterating through the possibilities, but there is a shortcut that will make this much easier.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 4, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #186: The Impossible Zoo

Welcome to Gene’s Impossible Zoo. The zoo has some four-legged animals (exactly one-half of the number of two-legged animals). The number of two-leggers is exactly one-half of the number of zero-legged animals (often called fish and snakes). These are all of the animals, and they have a total of 200 legs.

It is not called an impossible zoo for nothing. Why is the description above self-contradictory?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, December 28, 2016 at noon Pacific Time. I will post the answer shortly after.