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Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

  1. My favourite number has two digits and an odd number of divisors. The sum of the digits is 13. What is my favourite number?
  1. Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey about potential changes to next year’s schedule. Of students selected for the survey, 1/4 were freshmen and 1/3 were sophomores. Half of the remaining selected students were juniors. If 336 students were selected for the survey, how many were seniors?
  1. The diameter of the cutting wheel on a manual can opener is ¾ of an inch and the diameter of a can of peaches is 2½ inches. How many times will the cutting wheel turn when opening the can?
  1. The area of the floor of area rectangular room is 315 sq. feet. One wall is a rectangle of 120 sq. feet, and the other wall is a rectangle of 168 sq. feet The ceiling and the floor are parallel, how many cubic feet are in the volume of the room? (Note: all dimensions are whole numbers.)



There are more than one way of doing these puzzles and may well be more than one answer.  Please let me and others know what alternatives you find by commenting below.  We also welcome general comments on the subject and any feedback you'd like to give.

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Last month's solutions
  1. There are 10 points equally spaced around the circle with interconnecting lines drawn between them.
    1. How many lines are needed to draw the 10 point pattern shown below?
    2. How many lines would you need for 50 points on the circle?
    3. How many lines would you need for 100 points on the circle?

Solution: You can either try counting the lines in the diagram, or, use this handy short-cut formula, n*(n-1)/2

Using the formula n*(n-1)/2 where n = the number of points on the circle:

  1. n = 10, n*(n-1)/2 = 10*(10 – 1)/2 = (10 * 9)/2 = 45 lines
  2. n = 50, n*(n-1)/2 = 50*(50 – 1)/2 = (50 * 49)/2 = 2,450/2 = 1,225 lines
  3. n = 100, n*(n-1)/2 = 100*(100 – 1)/2 = (100 * 99)/2 = 9,900/2 = 4,950 lines

This formula can also be used for counting the number of individual handshakes in a group, one time per pair of individuals and is created as follows: If you have n points on a circle, each point would have (n-1) lines or connections with each of the other points on the circle except itself. The total lines for all points (n) would be n*(n-1) and since each pair of points also has a duplicate reverse connection (i.e.., x to y and y to x), then n*(n-1) must be divided by 2 to provide the final summing formula of n*(n-1)/2. A good formula to remember.

  1. In 2015 the populations of City X and City Y were equal. From 2010 to 2015, the population of City X increased by 20% and the population of City Y decreased by 10%. If the population of City X was 120,000 in 2010, what was the population of City Y in 2010?


x = Population of City X in 2015
x = 120,000 x 1.2 = 144,000


y = Population of City Y in 2010
y = 144,000 / 0.9 = 160,000

  1. Two bicycles start at the intersection of two perpendicular roads. One rides west at a rate of 9 miles per hour, while the other rides south at a rate of 12 miles per hour. If both traveled in the same plane, how many miles are they in the shortest distance between them at the end of 3 hours?


Using Pythagorean theorem:
a² + b² = c²  or  (27)² + (36)² = x²
x² = 729 + 1296 = 2025
x = √(2025) = 45 miles

  1. The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns £60 a performance for every 12 people attending. The performer pays 43% of the money earned to pay the organizer’s costs in putting on each performance. The rest of the money earned is the performer’s profit.
    1. What is the profit that the performer makes at a performance where 48 people attend?
    2. If the organizer receives £7.50 per person, per performance, what is the profit that the organizer make per performance?

Let x = the profit that the preformer makes.
Then, x = (4 * 60) * (1.00 – 0.43) = 240 * 0.57 = £136.80

Let y = the profit that the organizer makes.
Then, y = (48 * 7.50) – (4 * 60) = 360 – 240 = £120


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