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 #233: Friends’ Block

Five friends (Allison, Beth, Bob, Sue, and Tom) live in consecutive houses on the same side of one block of an east-west street. There are only the five houses on that side of the block. From the clues, determine who lives where.

Bob does not live at either end of the block.

Exactly one girl and one boy live next to Sue.

Tom lives west of Beth.

Bob lives east of Allison.

Usually, the friends meet at Sue’s because the total distance everyone has to travel to get there is lower than that for any other of the five friends.

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, November 22, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #232: Hugs and Kisses

Having survived the zombie apocalypse of last week, you are sending auntie Lucinda a card to let her know you are sort of OK. You have a limited supply of hugs and kisses: two O’s and three X’s. You will send her at least two. If the order does not matter—XXO and OXX would be considered the same—how many possible combinations do you have to choose from?

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, November 15, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #231: Zombies

Being an editor requires a certain amount of brains. The zombie apocalypse has struck Kamloops, and the zombies are going after the smart people first.

Let us join Sean Brady, editor of The Omega (the TRU student newspaper), as from his well-fortified office, he fights off a small band of zombies. There are four zombies. Three of them could each alone break through Sean’s defences in eight hours. The fourth zombie could do so alone in six hours.

Sean has called the police, but not surprisingly, they are busy.

One hour into the battle, Sean scores a lucky hit and takes out an eight-hour zombie. He does not manage to do any other damage that affects their ability to break through.

Exactly two hours after he called the police, they show up.

Do they find Sean still fighting and quickly despatch the zombies with rather more effective weapons than dictionaries and writing guides? Or maybe, the zombies have eaten Sean’s brain and have gone off to the Kamloops This Week office to see about munching on Christopher Fould’s brain? Which is it?

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, I will post the answer shortly after.

Puzzle #230: Even More Marbles

You have some marbles. Each is of one colour of red, orange, yellow, green, blue, and violet. You have one to nine of each colour with a different number of each colour. Given the following clues, how many of each colour do you have?

1) The number of red plus yellow plus violet equals the number of orange plus green plus blue.
2) The total of the number of red, orange, and yellow marbles is the same as the total of the number of marbles of some other colour.
3) The number of orange, green, and blue marbles are all odd.
4) There are fewer red marbles than any other colour.
5) There are two more blue marbles than green marbles.
6) There are more violet marbles than any other 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, November 1, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #229: Follow the Logic

Start with the number 7. Then follow these steps in order.

Step 1: If it is true that arutta, then add 5; if not, add 7.
Step 2: If it is true that budrist, then multiply by 2; if not, multiply by 3.
Step 3: Subtract twice the number you added two steps ago.
Step 4: Divide by two.

Your answer is a two-digit prime. Is arutta true, and is budrist true?

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, October 25, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #228: Frozen Yummy II

The yummy, chocolate-coated, ice cream thing on a stick that you – OK, OK, I – have been buying costs $4.20 at the local store near where I work. No, I forgot about the tax; it costs $4.45.

How many ways are there to pay $4.45 with exact change using the usual Canadian coin denominations (nickel, dime, quarter, loonie, and toonie)? Avoiding boredom once again, how many combinations consist of six or fewer coins?

[Hint: You can save yourself some effort if you look at the problem in the right way. Is this the same way as in the previous problem?]

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, October 18, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #227: Frozen Yummy

The yummy, chocolate-coated, ice cream thing on a stick that you – OK, OK, I – have been buying costs $4.20 at the local store near where I work.

How many ways are there to pay $4.20 with exact change using the usual Canadian coin denominations (nickel, dime, quarter, loonie, and toonie)? Wait; that would be boring. How many combinations consist of six or fewer coins?

[Hint: You can save yourself some effort if you look at the problem in the right way.]

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, October 11, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #226: What is the Rule?

If red is better than blue, starting better than quitting, something better than nothing, water better than wine, failure better than success, area better than volume, fast better than slow, and fast better than rapid, which is better: math or money? Why?

[Clue: The rule has to do with the spelling of the words.]

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, October 4, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #225: Textbooks

You are taking five courses, one each in Accounting, Biology, Computing Science, English, and Japanese.

The cost of the Japanese textbook is twice that of the English textbook. The cost of the Computing Science textbook is twice that of the Accounting textbook. It is also four-thirds of the cost of the Japanese textbook. The Chemistry textbook cost ten dollars more than the average cost of the other four textbooks.

If each textbook cost an exact number of dollars and you spent somewhere in the $300’s, how much did each textbook cost, and what is the total?

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, September 27, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #224: Fauxgo

Fauxgo is a language that I have just made up. (“faux” is French for false, and “go” is Japanese for language.) Fauxgo has three letters: A, B, and C. Words must be formed using certain rules:

An A can not immediately follow a pair of the same letter (eliminating “CCA”).
An A can not be immediately followed by a B (eliminating “CAB”).
A B must be doubled (eliminating “CBA”).
A C can not immediately follow a pair of the same letter (eliminating “BBC”) or follow two A’s that are at any point previous in the word (eliminating “ACAC”).
Three of the same letter in a row is not permitted (eliminating “AAA”).

Given these rules, what is the longest possible word in Fauxgo?

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, September 20, 2017 at noon Pacific Time. I will post the answer shortly after.