**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

After a day at the races, four friends (A, B, C & D), compared their winnings and losses and found that between them they had broken even. D had lost twice as much as B won. B won £10 less than A lost, and A had lost £20 less than C won. How did each of them do?

## Puzzle Two

“And now over to Brian Barber who can tell us what happened.”

“Thank you, Kim. It was truly gripping race with a lot of money on the favourite Don Quay. The four horses jumped the last fence in a bunch with Known Hope in second, but as they ran up to the finish line the leader at the last fence faded to third place. Also Ran improved one place from the last hedge to the finish line and Always True brought up the rear.”

What was the order over the last fence and at the finished line?

## Puzzle Three

Write the numbers 1, 3, 5, 7, 9, 11 and 13 in the circles so that each line of three numbers adds up to 21.

## 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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##### Last month's solutions

## Puzzle One

The price of an item was increased by 25% and later decreased by 25%, which makes the price of the item $375. What was the original price?

**Solution:**

Let p = the original price

Then, 1.25 x 0.75 x p = 375

p = £400

## Puzzle Two

If 3/4 is Peter’s salary is equal to 2/4 of Mary’s salary. What is Peter’s salary if Mary’s salary is £120,000?

**Solution:**

Let: Peter’s Salary = p

Then, ¾ x p = ½ x 120,000

p = 4/3 x 60,000 = £80,000

## Puzzle Three

418 marbles are initially shared among three kids A, B and C. A got half the amount of C’s share which is 3 times B’s share. If A now wins 35 marbles from B and loses 8 marbles to B in a game of marbles how many marbles do each now have?

**Answer:** A ends up with 141 marbles, B ends up with 84 marbles, and C has 193 marbles

**Solution:**

Let x = C’s share

Givens:

A’s share = 1/2 of C’s share, so A’s share = x/2

C’s share = x = 3 x B’s share, so B’s share = x/3

418 = A + B + C = x/2 + x/3 + x = (11/6)(x)

Therefore:

x = (418)(6/11) = (38)(6) = 228 (or C’s share)

B’s share = x/3 = 228/3 = 76 marbles

A’s share = x/2 = 228/2 = 114 marbles

A + B + C = 114 + 76 + 228 = 418

If A now wins 35 marbles from C, but loses 8 marbles to B, then

A now has 114 + 35 – 8 = 141 marbles

B now has 76 + 8 = 84 marbles and

C now has 228 – 35 = 193 marbles

Checking answers, A + B + C = 141 + 84 + 193 = 418

## Puzzle Four

There is a three-digit number. The second digit is four times as big as the third digit (no zeros) while the first digit is three less than the second digit. What is the three-digit number?

Answer: 582

**Solution:**

Let:

x = 1st single digit number

y = 2nd single digit number

z = 3rd single digit number

n = total 3-digit number where no two digits are the same or zero.

Given:

a) 100x + 10y + z = n

b) y = 4z

c) x = y – 3

d) z <= 3 (or 0, 1, 2, or 3)

z can = 1 or 2 but not = 0 or 3 because of step b) and y must be a single digit non zero.

If z = 1, then y = 4 from step b) and x = 1 from step c); x & z can not be the same value or 1)

Therefore, z = 2, then y = 8 from step b), x = 5 from step c) and n = 582 per step a).

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