### Brain Teasers

# Five 5`s

How can five 5`s equal 31?

### Answer

5x5+5+5/5 (or five times five plus five plus five-fifths)=31Hide Answer Show Answer

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## Comments

Nov 21, 2001

Or use base 8

5+5+5+5+5 = 25

5+5+5+5+5 = 31

**base 10**5+5+5+5+5 = 25

**base 8**5+5+5+5+5 = 31

How does base 8 work?

In base 8, each place to the left is worth 8 times more than the one to its right (in the usual notation it's 10 instead of . ----- So, in base eight, the only digits are 0 1 2 3 4 5 6 7. Eight is written 10. 30 is three times eight, i.e. twenty-four. 31 is twenty-five. 100 is eight times eight, i.e. sixty-four.

I got 31 by placing a decimal point in front of two of the fives, but I'm pretty sure that wasn't allowed...

5 X 5 + 5 + .5 + .5 = 31

Oh well, it was fun anyway.

5 X 5 + 5 + .5 + .5 = 31

Oh well, it was fun anyway.

Subtox, that was a good alternate solution!

(Old math teacher!)

(Old math teacher!)

I got the expected solution, but I always like to get one extra:

(5! + 5 + 5) / 5 + 5 = 31

(5! + 5 + 5) / 5 + 5 = 31

5^2+5^1+5^0

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