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 #214: Cookies

Allan, Bobby, and Tammy each have some cookies. Bobby has two fewer than twice as many as Allan has. Tammy has six more cookies than Allan has. They got those cookies by splitting up a package of twenty-four cookies.

How many cookies does each 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, July 12, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #213: Found Money

Kathy, Larry, Mona, Neil, and Olivia each recently found a different amount of money. The amounts were $5, $10, $15, $20, and $40 though not necessarily in that order.

Mona found an exact multiple of the amount that Larry found.
Olivia found an exact multiple of the amount that Kathy found.
Larry found an exact multiple of the amount that Neil found.

How much did each find?

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, July 5, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #212: Magic Square

A 3-by-3 magic square contains the integers from 6 to 14.  (Each row, column, and diagonal adds up to the same number.)

Given the clues following, what integer is in each square?

The number in the top-right corner square is 10, 11, or 12.

The corner squares’ values are either all odd or all even.

The bottom-center number is 7, or 14, or maybe 13.

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 28, 2017 at noon Pacific Time. I will post the answer shortly after.

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.