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 #203: Holding Marbles

Fiona, Len, and Nancy are each holding two marbles, one in each hand. The marbles are red, green, and blue, and there are two of each colour. Fiona, Len, and Nancy are standing from left to right in that order. None of them are holding marbles of the same colour, nor are two marbles of the same colour in adjacent hands.

Fiona is holding a blue and a green marble. Len is holding a red marble in his right hand. Nancy is not holding a green marble in her right hand.

If not everyone is holding a marble in his/her left hand whose colour name comes before in the alphabet the colour name of the marble in her/her right hand, who is holding which marbles in which hands?

(Never mind whether left means the person’s left or on your left, etc. Who needs that confusion? You are looking at them from behind so these are the same.)

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, April 26, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #202: Weird Coins

You have a bunch of three types of coins denominated in dinero. Ashuls are worth 7 dinero each, bindins are worth 5 dinero each, and culkies are worth 11 dinero each.

If you wanted to pay for something exactly in dinero and getting change is not allowed, what is the largest amount in dinero that you can not express with some combination of ashuls, bindins, and culkies?

(For example, 21 dinero can be expressed as 3 ashuls or 2 bindins and 1 culkie, but 8 dinero can not be expressed in terms of the three coin values.)

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, April 19, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #201: Hotdogs

It is time to start your training for summer hotdog eating. Off you go to the local convenience store to work your way through the many combinations of toppings. LCS has the following toppings: mustard, relish, ketchup, chili, cheese, onion, garlic, and peppers.

If you can only have up to two of mustard, relish, and ketchup and at most one of onion, garlic, and peppers, how many different hotdog topping combos can you create?

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, April 12, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #200: Whodunnit?

Four suspects were questioned by police about a recent crime. It is known that one of them must have done it. Each suspect made two statements. One person told the truth both times, one person lied both times, and the other two told the truth once and lied once. Given the following statements, whodunnit?

Al: (A1) I did not do it.
(A2) Di did it.
Bo: (B1) Al or Ci did it.
(B2) Di is being totally truthful.
Ci: (C1) Bo is totally lying.
(C2) Di did not do it.
Di: (D1) I did not do it.
(D2) Al did 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, April 5, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #199: Siblings

Susan has twice as many brothers as sisters. Her brother, Tom, has twice as many sisters as brothers. How many male siblings are there, and how many female siblings are there in Susan’s and Tom’s family?

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 29, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #198: Buckets

You have two buckets. One holds six liters, and the other holds seven liters. There is no way to measure partial bucketfuls accurately, and you want five liters in one of the buckets. You can fill a bucket fully from the water source, and you can pour from one bucket to the other (either the entire contents of the first bucket or until the second bucket is full).

How can you measure five liters?

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

Puzzle #197: The Chase

There are six dogs (Bowser, Fido, Lady, Rex, Prince, and Rover) and six cats (Fluffy, Ginger, Kitty, Princess, Puss, and Tiger).

Pair each dog with a cat to chase. No dog is paired with more than one cat. No cat is paired with more than one dog.

How many unique combinations of dog-cat pairs are there? (A combination is a set of six dog-cat pairings.)

The chase is on.

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

Puzzle #196: Books

Georgina has 1000 books. They consist of 500 science fiction books, 400 horror, and 300 romances. There is obviously some overlap, and every book is in at least one of the three categories.

Twice as many books are horror-romances as are sf-romances. (Warning: An sf-horror-romance is in both groups.) She has four times as many romance-only books than she has sf-romance-only. She has the same number of sf-horror-only as she has sf-romance.

How many books of each combination of the book categories does she have?

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 8, 2017 at noon Pacific Time. I will post the answer shortly after.

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.