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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.

## Puzzle One

How many 3-digit numbers are divisible by 7?

## Puzzle Two

In a certain class, 60% of the students are female and 40% are male. If 80% of the females and 70% of the males get A grades, what percentage of the class gets an A?

## Puzzle Three

Certain number of persons are standing in a row. Jake is 18th from the left end and Tiny is 23rd from the right end. If they interchange their positions, Tiny becomes 33rd from the right end.  How many persons are there in the row?

## Puzzle Four

A ship is sailing north at a speed of 20 km/hour. A second ship directly south of this is sailing east at a speed of 15 km/hour. How fast are they traveling apart?

## Feedback

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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## Puzzle One

Two trains are heading towards each other on parallel tracks The first train is traveling at 60 mph and the second train is traveling at 40 mph. The distance between the two trains is 500 miles. If they started at the same time, how long will it take before they begin to pass each other?

Solution:

The trains are approaching each other at 100 mph, so will take 5 hours to cover the 500 miles.

## Puzzle Two

If the third term of an arithmetic sequence is 15 and the eighth term is 40, what is the 20th term?

Solution:

15/3 = 5, 40/8 = 5; therefore, 20 * 5 = 100

## Puzzle Three

The sum of two numbers is 25. If three times the first number is subtracted from twice the second number, the result is 7. What are the two numbers?

Solution:

If the 1st number is x and the second number is y, then
x + y = 25; y = 25 – x
2y – 3x = 7; 2(25 – x) – 3x = 7
Therefore, 50 – 2x – 3x = 7; 5x = 43
So, x = 8.6 and y = 25 – 8.6 = 16.4

## Puzzle Four

Find the numerical equivalent for the following alphameric expressions to satisfy the equations below:

a) XYZ + XZY = ZYX, Solution: 459 + 495 = 954

b) EAT + THAT = APPLE, Solution: 419 + 9619 = 10038