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 #211: Marbles

You have some one-colour marbles, each one of red, orange, yellow, green, blue, and violet. No two marble counts of a colour add up to twelve. There is at least one and no more than nine of each colour. There is exactly one sequence of three consecutive marble counts of a colour (like 4, 5, and 6). The number of marbles of each colour is different. Only one marble count of a colour is a square.

What are each of the six marble counts? Note that, in this puzzle, you do not need to figure out which count goes with which 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, June 21, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #210: Class Groups

There are eight students in a class. There is a project assignment which is to be completed by teams of two students. How many ways can the students be grouped into four pairs?

(Warning: 1&2, 3&4, 5&6, 7&8 and 4&3, 7&8, 2&1, 6&5 are the same grouping.)

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, June 14, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #209: Olde Money

With decimalisation in 1971, British money became much more sane/boring. This puzzle uses the old system of coins: 1/2 d., 1d., 3d., 6d., 1/-, 2/-, 2/6, and 5/-. (The values are, respectively, 1/2, 1, 3, 6, 12, 24, 30, and 60 pence. There might have been a few other varieties – it did change over time – but we will ignore them.) How many ways can you make change that adds up to 1 pound (240 pence) if you can use no more than two of any one denomination?

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, June 7, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #208: Seventy-Five Cents

If you have five quarters, five dimes, and five nickels, how many ways can you count out seventy-five cents in change?

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, May 31, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #207: The Chicken Race

One boring afternoon, you set up a chicken race. The chickens are Abby, Bria, Cora, Dora, and Elsa.

Neither Abby nor Bria placed fourth. Cora placed the same number of places ahead of Bria as Dora placed ahead of Abby. Dora placed second. Elsa placed in the top three. There were no ties.

How did each chicken place?

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, May 24, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #206: Stepping Up

You are about to go upstairs. The stairs have six steps plus the top so you will have to climb seven steps. How many ways can you make these seven steps if you can take one or two steps at a time?

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, May 17, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #205: SOS

Consider a tic-tac-toe grid. Instead of three X’s or O’s, how many ways can you put SOS in a horizontal, vertical, or diagonal 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, May 10, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #204: $17.35

How many ways can you express $17.35 in Canadian bills and change?

There is one additional proviso: any combination may not have more than two of any denomination.

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, May 3, 2017 at noon Pacific Time. I will post the answer shortly after.

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.