perplexus.info :: Numbers : six and thirteen

six and thirteen (Posted on 2018-03-15)

Part one:

Compose number 6 with each digit using the digit only three times (Ex: 6=2+2+2) Allowed basic operations (+,-,*,/), sqrt and factorial (no others).

Part two:

Get number 13 using only number 2 three times. Allowed basic and not-basic operations.

No Solution Yet Submitted by armando

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| Comment 3 of 9 |

I've seen part two before. The trick is to use a combination of base-2 logs and square-roots. In fact you can represent any integer in the same fashion.

If n is the desired integer, n = - log_2(log_2(√√...(2)) where the number of sqrt operations is n.

So 13 = - log_2(log_2(√√√√√√√√√√√√√2)) =

- log_2(log_2(2^(2^-13))) = - log_2(2^-13) = 13

Posted by xdog on 2018-03-15 12:33:54

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