# B Four 2s puzzle

1. Feb 8, 2017

### Auto-Didact

NB: This is a blatant ripoff of this other thread.

The challenge is to express a whole number using the number 2 precisely 4 times, and using only well-known mathematical symbols and no variables. How high can you go?

2. Feb 8, 2017

### Staff: Mentor

The same trick as in the other thread works here. $\log_2 \sqrt 2 = \frac{1}{2}$ to get the base 1/2, the powers of 1/2 can be constructed in the same way as with 4.

Generalized in that way (so we don't need sqrt(4)/4), you can use the approach with every positive real number apart from 1. Negative numbers work with the magnitude (|-4|). Only 0, 1 and -1 don't allow that approach.

If you count the exponential function as well-known function, you can use exp(exp(0)) and exp(1) to get suitable numbers even in the three exceptions from above. Several other functions work as well, of course, you just have to get any real number that is not -1, 0 or 1.

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