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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. 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?

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?

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.

 

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Last month's solutions

Challenge 1

What day comes three days after the day which comes two days after the day which comes immediately after the day which comes two days after Monday?

Solution: Working backwards:

M T W T F S S M T        Answer = Tuesday 

Challenge 2

The sum of four numbers is 60. One of the numbers is 50% more than the sum of the other three numbers. What is the value of this number?

Solution:

Let y, z, and w represent the three other numbers.

Given: x + y + z + w = 60 and  x = 3/2 (y + z + w)

and, (y + z + w) = 2/3 x

Then,  x + (y + z + w) = 60,  x + 2/3 x  = 3/3 x + 2/3 x = 60

Therefore, 5/3 x = 60  and x = 3/5 * 60 = 36

 

Challenge 3

A circle is circumscribed about a square (as shown below). A second circle is inscribed in the square. What is the ratio of the area of the smaller circle to the area of the larger circle? (Note: express your answer as a common fraction.)

 

Let r1 = radius of smaller circle and

      r2 = radius of larger circle, where r2 = r1 √2

Then, the ratio of the smaller to the larger circle areas =

π(r1)² / π(r2)² = π(r1)² / π(r1 √2)² = 1(r1)² / 2(r1)² = ½ (or 1 to 2)

 

 

 

 

 

 

 

 

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