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.
Puzzle 1In our Community Centre, there is a huge swimming pool with four pipes that can be used to fill the pool.
If all four pipes are used simultaneously, how long will it take to fill up the pool completely? |
Puzzle 2A farmer wants to plant 19 trees in 9 rows with 5 trees in a row. Show how the farmer can do this? |
Puzzle 3Kim threw some darts at this dartboard. Every dart landed on a number on the board and she scored exactly 100. If numbers can be used more than once, how many darts did she throw to score 100 and which numbers did she land on? |
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Last month's solutions
Challenge 1
A solid cube of 6-unit sides is first painted pink and then cut into smaller cubes of 1-unit sides. How many of the smaller cubes have paint on exactly 2 sides?
Solution:
The large cube has12 edges and each edge consists of 6 smaller cube edges. Eliminating each of the 4 smaller corner cubes (which will have 3 pink sides), each large cube edge then has 4 smaller cube with only 2 pink painted sides on them.
Therefore, 12 * 4 = 48 smaller cubes with only 2 sides painted pink.
Challenge 2
Ann and Dee are sisters. Ann is 4 years old and Dee is 13 years old. What ages will each be when Dee is twice as old as Ann?
Solution:
Let x = number of years to double the ages between Ann and Dee
or, 2 * Ann’s Age = Dee’s Age
Then, 2(4 + x) = (13 + x)
8 + 2x = 13 + x
x = 5 yrs.
Therefore, Ann’s age will be = 4 + 5 = 9 yrs.
And, Dee’s age will be = 13 + 5 = 18 yrs.
Or, an easier approach:
Ann Dee
4 ………. 13
5 ………. 14
6 ………. 15
7 ………. 16
8 ………. 17
9 ………. 18
10 ………. 19
Challenge 3
In the figure below, the radius of circle B is three-fourths the radius of circle A. The distance from centre A to the circumference of circle B is 3, and the distance from centre B to the circumference of circle A is 2. What is the area of the smaller circle? (Note: Use π = 3.14)
Solution:
Let: Radius of Circle A = 3 + x and: Radius of Circle B = 2 + x
Given: (2 + x) = ¾ (3 + x)
Thus, 2 + x = 9/4 + ¾ x
x – ¾ x = 9/4 – 8/4
¼ x = ¼
x = 1
Therefore, Area of Circle B = π r² = π (x+2)² = π * 3² = 9π, or 9 * 3.14 = 28.26