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 = 41/64
double = 81/32
take away 3 = 51/32
times 4 = 201/8
subtracting 1/8 gives 20, as required.
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