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September – 2021 Challenge

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.

Click here to download the printable version

 

  1. 25 drag racers come to the track to determine the top 3 cars by speed.
    Unhappily all the timing mechanisms are broken, so the races must be determined, head-to-head. Now the track has 5 lanes, and so 5 cars can race at a time. The question is what is the minimum number of races to determine the top 3 drag racers?
  1. What is the distance from town A to town G, if town A is eleven miles north of town B, town B is eight miles east of town C, town D is seven miles south of town C, town E is five miles west of town D, town F is three miles north of town E and town F is seven miles east of town G?
  1. Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost £75 each, and tickets to sit on the lawn during the concert cost £40 each. Organizers of the concert announced that 350 tickets had been sold and that £19,250 had been raised through ticket sales alone. What number of tickets were sold for the concert’s bench seats (B), and for the lawn seats, (L)?
  1. A dress on sale in a shop is marked at £65. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay?

 

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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. My favourite number has two digits and an odd number of divisors. The sum of the digits is 13. What is my favourite number?

Solution:

The only two-digit numbers that add to thirteen is 49, 58, 67, 94, 85 and 76.

Of these, the only number with an odd number of divisors is 49 (7 x 7) (1 divisor). The other numbers either have no divisors or an even number:  58 (2 & 29), 67 (none), 94 (2 & 47), 85 (5 & 17) and 76 (2, 4, 19 & 38)  (none, 2 or 4)

Therefore, my favourite number is 49 (with only one divisor).
  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?

Solution:

Let x = number of senior students

and y = sum of freshmen and sophomore students

Then, y = ¼ (freshmen) + 1/3 (sophomores)

           y = ¼ (336) + 1/3 (336) = 84 + 112 =196

and    x = 336 – y – ½ (336 – y) = 336 – 196 – ½ (140) = 70 senor students
  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?

Solution:

Circumference of cutter = πD1 = ¾ π

Circumference of can = πD2 = 2½ π

Number of turns = πD2 / πD1 = 2½ π / ¾ π =

5/2 ÷ ¾ = 5/2  x  4/3 = 20/6 = 3 & 1/3 turns
  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.)

Solution:

For the floor area of 315 one dimension must end in a 5  (i.e., 5, 15, 25, etc.).

The best fit is 15 and therefore the floor dimensions would then be 15 ft. x 21 ft.

Then, for one side area of 120 sq. feet wall, one dimension must be either the 15 ft. or 21 ft.

The best fit is 15 and therefore the the wall dimensions would then be 15 ft. x 8 ft.

And for the other side area of 168 sq. feet wall, one dimension must be 21 ft.

The other wall dimensions would then be 21 ft. x 8 ft.

Therefore, the volume for the room = 15 x 21 x 8 = 2,520 cubic feet.

 

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