Puzzle 1
You have a very large number of generic plastic building blocks, each in the shape of a cube.
Think about how many cubes you would need in order to construct a giant cube with 16 small cubes along each edge.
If you were to then remove the outside layer, how many small cubes would you have removed?
Puzzle Copyright © Kevin Stone
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Hint
How large would the smaller cube be?
Answer
1,352 small cubes.
Reasoning
The original large cube with 16 small cubes along each edge would require 16 x 16 x 16 = 4,096 small cubes.
Removing the outside layer would leave a large cube now with 14 small cubes along each edge (which requires 14 x 14 x 14 = 2,744 small cubes).
It isn't 15 small cubes because you're removing both ends of an edge.
Therefore, you have removed 4,096 – 2,744 = 1,352 small cubes.
Puzzle 2
Can you highlight exactly three numbers that add to 19?
Note: this puzzle is not interactive, and the numbers cannot be clicked.
Puzzle Copyright © Kevin Stone
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Hint
You have to highlight three numbers.
Answer
6 + 1 + 12 = 19.
The puzzle didn't ask for three digits to be highlighted!
Puzzle 3
Every year, just before my birthday, I open my money box to see how much money I have saved.
Imagine my surprise when I found exactly £49.58 made up of equal numbers of 2p, 5p, 10p and 20p.
How many of each coin did I find?
Puzzle Copyright © Kevin Stone
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Hint
Remember that you have the same number of each coin.
Answer
134 of each coin.
Reasoning
We have equal numbers of 2p, 5p, 10p, and 20p.
And 2p + 5p + 10p + 20p = 37p.
There are 134 lots of 37p in £49.58.
Double-Checking
134 x 37 = 4958.
Puzzle 4
What number comes next in this sequence:
1 23 124 1251 26127 128129 ?
Puzzle Copyright © Kevin Stone
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Hint
Try removing the spaces from the sequence.
Answer
1301311 or 1210121.
Reasoning
Removing spaces from the original sequence gives:
1 23 124 1251 26127 128129
123124125126127128129
Now adding spaces back in, in the correct place:
123 124 125 126 127 128 129
The next few terms could be:
130 131 132
or
1210 1211 1212
Add these to the end:
123 124 125 126 127 128 129 130 131 132
or
123 124 125 126 127 128 129 1210 1211 1212
Remove the spaces again:
123124125126127128129130131132
or
123124125126127128129121012111212
Now break the sequence into chunks of increasing size:
1 23 124 1251 26127 128129 1301311
or
1 23 124 1251 26127 128129 1210121
So the missing term is 1301311 or 1210121.
