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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 1

You have three darts with each go to score 42. Aim at this target and work out how many different ways there are to make the score. Assume each dart scores and once three numbers have been used, the same three combinations cannot be used again in any order. How many combinations are there to score 42?

## Puzzle 2

You have 25 sticks standing upright in a circle, numbered 1 to 25 clockwise. Starting with stick 1 and then rotating in a counterclockwise direction around the circle, knock over every third stick in each rotation of the circle (i.e., 24, 21, 18, etc). Keep rotating around and around the circle knocking over every third stick standing until only one stick remains standing. What will be the number of the last stick standing?

## Puzzle 3

Four playing cards, one in each suit, lie face down on a table. They are a three, four, five and six.

• The cards on either side of the four are black.
• The club is to the right of the three.
• The spade is to the left of the heart.
• The sum of the first two cards equals the sum of the last two cards.

Can you determine the cards’ suits and their order?

## 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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## Challenge One

Items of fruit are sold singularly in a supermarket. From the information below can you list the seven fruits in order of price, starting with the most expensive?

A banana costs less than a peach but more than a pear, a kiwi costs less than a pear and more than an apple, a pineapple is more expensive than a peach and a lemon costs more than a kiwi but less than a pear.

Solution:

A banana (A) costs less than a peach (B) but more than a pear (C). A kiwi (D) costs less than a pear (C) and more than an apple (E). A pineapple (F) is more expensive than a peach (B). A lemon (G) costs more than a kiwi (D) but less than a pear (C).

Since, A < B, A > C, D < C, D > E, F > B, G > D, G < C

So       A < B < F, A > C > D > E   and  C > G > D

So       F > B > A > C > D > E and  C > G > D

So       F > B > A > C > G > D > E

F – pineapple (Highest), B – peach, A – banana, C – pear, G – lemon, D – kiwi and E – apple (Lowest)

## Challenge Two

You have 25 sticks standing upright in a circle, numbered 1 to 25 clockwise. Starting with stick 3 and then rotating in a clockwise direction around the circle, knock over every other or second stick in each rotation of the circle (i.e., 4, 6, 8, etc). Keep rotating around and around the circle knocking over every second stick standing until only one stick remains standing. What will be the number of the last stick standing?

Solution:

Sticks in the Circle: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
After 1st CW pass around: 3, 5, 7, 9, 11,13, 15, 17, 19, 21, 23, 25, 2
After 2nd CW complete pass around: 5, 9, 13, 17. 21, 25
After 3rd CW complete pass around: 5, 13, 21
After 4th CW complete pass around: 5, 21
After 5th CW complete pass around: 21 (Last Stick Standing)

## Challenge Three

The empty boxes contain any of the number 1-9, and no empty box contains the same number as another empty box.

The three numbers in cells D1-3 equal the value of the top row minus the bottom two rows’ values.

The three numbers in A4, B4 and C4 equal the value of the left most column minus the values of the other two columns

The same principle applies to the diagonal from A1 to D4
Solve the puzzle by finding all of the missing numbers that satisfy all of the results as shown.

Solution: