# Eight eights Puzzle - Solution

## The Puzzle:

Using 8 exactly eight times to make a 1000.

a) Using only + - * /

b) Also allowing root symbols √, exponents ^, factorials !, and decimal points.

## Our Solution:

A) Using only + - * /
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By Shivani Dixit:
888 + 88 + 8 + 8 + 8

by Patrick Saunders:
(8(8(8+8)-(8+8)/8))-8

By Daryl S::
(888-8) + 8×(8+8) - 8
((8×(8+8))-((8+8+8)/8))×8
((8×(8+8))-((88/8)-8))×8
(8888-888)/8

By Manoj Kumar Nanduri:
8(8×8+8×8)-8-8-8

B) Also allowing √, ^, ! and decimal points.
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by Year 10 Set 4 at Lady Manners in Derbyshire:
8888/8.888

By Daryl S::
(8+((8+8)/8))^((8+8+8)/8)
(8+((8+8)/8))^((88/8)-8)

By Robert Veith:
(8888 - 8)/8.88
(8888 - 88)/8.8
(888.8 - 8.8)/.88
88.8/(.8888 - .8)
8.8/(.8888 - .88)
888.8/.8888
(8888 - 88)/8.8
(8888 - 8)/8.88
8.8/.88 X 88/.88
88.8/.888 X 8/.8
888/.888 X 8/8

AND because 10^3=1000 there are 144 solutions made by combining:

Ways to make 10 (using 4 8's):
(8.8/.88)
(88/8.8)
((8 + 8 - 8)/.8)
(8/(.8 + 8 - 8))
((88 - 8)/8)
(√(88/.88))
((8 + 8)/(.8 + .8))
(8 + 8/√(8 + 8))
((8 + 8)/8 + 8)
(√(8×8) + √(√(8 + 8)))
(8/8×8/.8)
(8(8 - 8)!/.8)

Ways to make 3 (using 4 8's):
((8 + 8 + 8)/8)
(√(√(8×8) + (8 - 8)!))
(√(√(8 + 8)) + 8/8)
(√(8 + 8) - 8/8)
(88/8 - 8)
((√(8 + 8)!/√(8×8))
(√(8 + 8) - (8 - 8)!)
(√(√(8 + 8)) + (8 - 8)!)
(√(8/.8 - 8/8))
(√(√(8×8) + 8/8))
(√(8/.8 - (8 - 8)!))
(√(8 + (8(8 - 8))!))
Puzzle Author: Shivani Dixit

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