Start with a number larger than 0, square it, add 4, double, take away 3, times 4 and finally subtract the original number.

If you were now left with 20, what number did you start with?

Puzzle Copyright © Kevin Stone

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Hint

A little algebra might help.

Answer

^{1}/_{8}.

Reasoning

If we convert the question to algebra, we have:

((n^2 + 4) x 2 – 3) x 4 – n = 20

Expanding the brackets and simplifying gives:

(2n^2 + 8 – 3) x 4 – n = 20

(2n^2 + 5) x 4 – n = 20

8n^2 + 20 – n = 20

8n^2 – n = 0 (*)

8n – 1 = 0

8n = 1

n = ^{1}/_{8}

In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.

Double-Checking

^{1}/_{8}

squared = ^{1}/_{64}

add 4 = 4^{1}/_{64}

double = 8^{1}/_{32}

take away 3 = 5^{1}/_{32}

times 4 = 20^{1}/_{8}

subtracting ^{1}/_{8} gives 20, as required.