Reasoning
Take the numbers in pairs, square the first, and reverse the digits.
1 1 (1 x 1 = 1, reversed is 1)
2 4 (2 x 2 = 4, reversed is 4)
3 9 (3 x 3 = 9, reversed is 9)
4 61 (4 x 4 = 16, reversed is 61)
5 52 (5 x 5 = 25, reversed is 52)
6 63 (6 x 6 = 36, reversed is 63)
7 94 (7 x 7 = 49, reversed is 94)
so we require:
8 46 (8 x 8 = 64, reversed is 46)
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Puzzle 6
I have a jar of sweets that contains 114 red, 35 blue, 67 green, and 9 yellow.
What chance do I have of picking a yellow sweet with my eyes shut?
Hint
There are more than 37, look at the different sizes.
Answer
There are 64 hexagon-type shapes in total.
Reasoning
37 single hexagons
+ 19 hexagons that contain 7 smaller hexagons
+ 7 hexagons that contain 19 smaller hexagons
+ 1 large hexagon that contains all of the smaller hexagons.
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Puzzle 8
My local shop wants to create a sign that says PUZZLES, and they have the following letters, each in a different colour:
P P P U U Z Z Z Z Z L L L L E S S
How many different ways can they make the sign?
Hint
There are 3 P's, so there are 3 different ways to start the word.
Answer
960.
Reasoning
Given: P P P U U Z Z Z Z Z L L L L E S S.
The order of the Z's is important. For example, we could chose a red one and a green one, so the order they appear in the sign has to be taken into consideration.
There are:
3 different P's that could be chosen.
2 different U's that could be chosen.
5 different Z's that could be chosen.
4 different Z's that could be chosen, as one has already been chosen.
4 different L's that could be chosen.
1 E that could be chosen.
2 different S's that could be chosen.
So there are 3 x 2 x 5 x 4 x 4 x 1 x 2 = 960 different ways to make the sign.
