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 #220: Borders

How many Canadian provinces have exactly four straight lines for their land borders? For the purposes of this puzzle, a straight line is a line that runs on a line of latitude or of longitude and is primarily land. (Rivers and lakes are not considered to violate this, but a salt water coast does.)

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, August 23, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #219: Still More Marbles

You have some marbles, each of one colour of red, orange, yellow, green, blue, and violet.

The number of green marbles is one-quarter of the number of all of the other marbles.
The number of blue marbles is the square root of the number of orange marbles. (A square root of a number is a number that multiplied by itself equals the original number. The square root of 4 is 2 since 2 × 2 = 4.)
The number of red marbles is the cube of the number of violet marbles. (27 is the cube of 3 as 3 × 3 × 3 = 27.)
The six numbers of marbles are all different, and each is in the range of one to nine.

Given the above clues, how many of each colour do you 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, August 16, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #218: The Job Offer

You have just been offered a job paying $50,000 per year. You have your choice of two different raise packages. Plan A is a raise of $2,000 per year after every year. Plan B is a raise of $950 per year after every six months. The maximum salary for the position is $60,000 per year.

Assuming you want to make as much money as you can, which plan should you take? Why?

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, August 9, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #217: Bleach

I encountered this problem at work recently.

You have some bleach which is 4.1% sodium hypochlorite (and thus 95.9% water). You need to dilute the bleach so it is 3% sodium hypochlorite.

If you start with 100 parts bleach, how many parts water (to the nearest integer) are needed to dilute to 3%? There is a simpler form that is close to 100:x; what is that?

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, August 2, 2017 at noon Pacific Time. I will post the answer shortly after.

Puzzle #216: Sandwiches

The local corner store has 12 sandwiches in the cooler. Five have corned beef, seven have cheddar cheese, and six have Swiss cheese. Each sandwich has at least one of the three ingredients, and there is at least one sandwich of each of the seven ingredient combinations. Exactly three sandwiches contain both types of cheese. Two sandwiches contain all three ingredients.

How sandwiches are there of each type?

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

Puzzle #215: Divvying Up Candy

Six kids were given a bag of candy and told to split it evenly. When they tried to do so, there was one piece of candy left over. There would have been one piece of candy left over if there were only two, three, four, or five kids, too. What is the minimum number of pieces of candy there could be in the bag if there were at least ten pieces of candy?

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

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.