Puzzle 1
What number comes next in this sequence:
2 5 9 19 37 ?
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Hint
The sequence involves doubling in some way.
Answer
75.
Alternately double plus one, double minus one.
Puzzle 2
Can you find three consecutive even numbers that …
… total 85,008 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
Try starting with the cube root of the number.
Answer
42, 44, and 46.
Reasoning
As we require 3 numbers that are multiplied together, we can start with the cube root of 85,008 ≈ 43.97.
We can now check that 44 divides 85,008 exactly: 85,008 ÷ 44 = 1,932, which means that 44 is likely to be one of the numbers.
And as we know that we need consecutive even numbers, we soon find 42 and 46 as the remaining numbers.
Double-Checking
42 x 44 x 46 = 85,008.
Puzzle 3
If I give you seven apples, you will then have five times as many as I would then have.
However, if you give me seven apples, we will then both have the same number of apples.
How many apples do I currently have?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
I have 14 apples and you have 28 apples.
Reasoning
We can work this out with a little algebra. I have A apples and you have B apples, then
[1] 5 x (A – 7) = B + 7
[2] A + 7 = B – 7
From [1] we have:
5A – 35 = B + 7
[3] 5A = B + 42
From [2] we have:
[4] A + 14 = B
We can then use [4] in [3] to give:
5A = (A + 14) + 42
5A = A + 56
4A = 56
A = 14
Which gives B = 28 (by [4]).
