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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.

### 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?

### 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?

### 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) ## Feedback

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##### Last month's solutions

1. If Dave drove one-third of the distance on the first day, and 60 km on the second day, he figured out that he still had 40% of the trip to drive. What will be the total length of his trip, in kilometers?

Solution:

Let x = total length of trip

x = 1/3x + 60 + 2/5x
x – 1/3x – 2/5x = 60
15/15 x – 5/15x – 6/15x = 60
4/15x = 60
x = (60*15)/4
x = 225 km

2. A software company is selling a new game in a standard edition and a collector’s edition. The box for the standard edition has a volume of 20 cubic inches, and the box for the collector’s edition has a volume of 30 cubic inches. The company receives an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. How many standard edition games and collector’s edition games were ordered?

Solution:

Let s = standard edition games ordered (box size = 20 cu.in.) and c = collector’s edition games ordered (box size = 30 cu.in.)

Then, s + c = 75 or c = 75 – s
and, 20s + 30c = 1870 or 20s = 1870 – 30c

Therefore, 20s = 1870 – 30 (75 – s) = 1870 – 2250 + 30s
10s = 370
s = 37 (standard edition games ordered)
c = 75 – s = 75 – 37 = 38 (collector’s edition games ordered)

3. Each of the nine letters stand for a numbers (1 through 9, without repeats). Using the following clues, can you find the number that represents each letter A through I. a) In one diagonal, each number is a square.
b) D, C and I are odd numbers in ascending order.
c) G is the sum of A and F.
d) B is the product of E and H.
e) One row has consecutive numbers in some order.

Solution: 