# 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 #248: Blended Pets

Tom and Sabrina just got married. It is a blended family including the pets. There are three cats and two dogs. Tom and Sabrina each had had at least one pet. How many combinations of the premarital distribution of the numbers of cats and dogs are there?

[Note: This puzzle is not asking about specific cats and dogs but the number of them. For example, if Tom had had one cat and one dog and Sabrina had had two cats and one dog, that would be one combination. Who had had which pets is not relevant here.]

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 7, 2018 at noon Pacific Time. I will post the answer shortly after.

# Puzzle #247: Full House

From an ordinary 52-card deck of playing cards, you have just been dealt the ace of diamonds and the king of hearts. What is the probability that the remaining three cards will complete a full house? Answer to the nearest 0.01%.

[A full house is a poker hand of three of a kind and a pair.]

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 28, 2018 at noon Pacific Time. I will post the answer shortly after.

# Puzzle #246: Chocolates

You just bought a box of chocolates for your sweetie. There are fifteen chocolates. Looking down at the contents, you see they are arranged in three rows of five. According to the key, the arrangement of flavours is symmetrical, so the top row is the same as the bottom row, the left column is the same as the right column, and the second columns in from both sides are the same. There are six flavours of fillings: cherry, strawberry, and raspberry (the reds) and orange, lemon, and blueberry.

Given the following clues, what is the arrangement of chocolates?

1) Lemon are not on the corner, strawberry not on the inside, and cherry not next to lemon (not counting diagonal).

2) The number of lemon plus cherry is equal to the number of raspberry plus orange.

3) There is only one blueberry chocolate.

4) Fewer than one-half of the chocolates are red flavours.

5) There are four each of two flavours, two each of three flavours, and one of the last flavour.

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 21, 2018 at noon Pacific Time. I will post the answer shortly after.

# Puzzle #245: Treasure

You have just found some treasure. In a chest, there are some gold pieces, some silver pieces, and some copper pieces. A “friend” would like to know how much. You tell him that the number of copper pieces is seventeen less than five times the number of silver pieces, that the number of silver pieces is twelve less than five times the number of gold pieces, and that the treasure trove is as small as it could be.

While he is puzzling that out, you beat a hasty retreat muttering under your breath that sharing is for toys and ice cream.

How many of each coin type does your treasure have anyway? (I am just asking.)

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 14, 2018> at noon Pacific Time. I will post the answer shortly after.

# Puzzle #244: Buckets

You have two buckets. One will hold five liters of water, and the other will hold three liters. They have no markings. If you fill a bucket from the faucet, you must fill it full. If you pour from one bucket into the other, you can stop only when the first bucket is empty or the second bucket is full. You can also discard all of the water in a bucket.

How can you end up with four liters of water in the five-liter bucket?

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 7, 2018 at noon Pacific Time. I will post the answer shortly after.

# Puzzle #243: Five Nickels

You put five nickels in a bag. Four of them are ordinary nickels, but one is a fake with two tails sides. A random coin is drawn from the bag and placed on a table so only one side (which is randomly chosen) is showing. The coin shows tails. What is the probability that the coin drawn is not the fake?

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 31, 2018 at noon Pacific Time. I will post the answer shortly after.

# Puzzle #242: 2018

Using the digits 2, 0, 1, and 8, and the operations addition, subtraction, multiplication, division, and factorial, form expressions evaluating to the integers from zero to nine. For example, 2 + 0 + 1 + 8 = 11 and (2 + 1) × 8 – 1 = 23. The digits need not be used in the order 2-0-1-8, but you might try anyway. (In other years, I have come up with such solutions for all ten, but for this, I only managed five. Can you do better?)

[Zero factorial (written 0!) equals 1. For a higher integer n, n! = 1 × 2 × 3 × … × n. For example 3! = 6.]

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 24, 2018 at noon Pacific Time. I will post the answer shortly after.

# Puzzle #241: Fluffy to the Rescue

Your home is infested with feather dusters. Your cat, Fluffy, is going to save you from this horrible peril. This puzzle is dedicated to a cat I had—Tammy—who took out a feather duster; she was so proud. On an even-numbered day (day number by calendar), there is an 80% chance that Fluffy can take out one feather duster. On an odd-numbered day, the chance is 70%. There are four feather dusters. On days when you are not quick with the kitty treats, the chance is at most one-half of the figures given. Each day, there is a 25% that Fluffy will sleep all day. The wind outside gusts to up to 50 km/h.

Two questions: 1) What is the minimum number of days it will take Fluffy to take out all of the feather dusters? 2) What is the probability of three odd-numbered days in a row?

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 17, 2018> at noon Pacific Time. I will post the answer shortly after.

# Puzzle #240: The Bet

You are offered the following bet. You pay one dollar. Two coins are flipped. If they both come up the same, you win two dollars. If the first coin lands heads and the second tails, you lose one dollar. In the case of first tails and second heads, a third coin is flipped. If the third coin lands heads, you win five dollars; if it lands tails, you lose four dollars.

Should you take this bet? Why or why not?

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 10, 2018> at noon Pacific Time. I will post the answer shortly after.

# Puzzle #239: Wrong Number

The Talk Back Q&A figures in the 2017-12-19 issue of Kamloops This Week have an error. Supposedly, there were 591 votes on the question. 332 or 56% were yes and 41 or 44% were no. There were no other votes.

If exactly one of the five numbers is wrong, 1) which one is it and why and 2) what is the correct number?

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 3, 2018 at noon Pacific Time. I will post the answer shortly after.