My previous post “Can Two 2’s Produce 5?” showed a way to produce 5 using only two 2’s and any mathematical operations. Now, here’s another similar puzzle. Using eight 8’s and any mathematical operations and symbols, can you make them equal to 1000? There are several solutions.
When I asked this question to some of my friends, they were able to give me six basic solutions (though there are more):
(This solution has several variantions. Can you find them?)
One of them was smart enough to use square roots and factorials, so he was able to find four more solutions:
I have found more solutions which involve square roots and factorials. Can you find more?
This puzzle can be solved by producing 10³ using the 8’s:
If special mathematical symbols are employed, more solutions can be found:
Floor and Ceiling Functions:
Base 8 logarithm:
Finally, this solution involves base 8 numbers:
However, this is not an acceptable solution since the answer is in base 8 and 1000 in base 8 is equal to 512 in base 10. Any interested reader may try to find a valid solution using base 8 numbers.