## Express 6

I was given this puzzle at the last Gathering for Gardner.

Use arithmetic operations to express 6 using three identical digits. For each digit from 0 to 9 find at least one way to express 6.

For example, I can express 6 using three twos in many ways: 2 + 2 + 2, or 2 · 2 + 2, or 2^{2} + 2. But the problem doesn’t ask for many ways. One way is enough, but you need to do it for every digit. So nine more cases to go: 0, 1, 3, 4, 5, 6, 7, 8, and 9.

## George R.:

Well, I’ll try the easy ones first 🙂

22 May 2014, 11:43 am6*(6/6)

5+5/5

7-7/7

sqrt4 +sqrt4 +sqrt4

3*3 -3

sqrt (9*9)-sqrt9

(0! +0!+0!)!

(1+1+1)!

I don’t have a solution for 8’s yet.

## Tanya Khovanova:

George, that was fast. One more to go.

22 May 2014, 12:20 pm## Konstantin Knop:

8 – sqrt(sqrt(8+8))

22 May 2014, 1:04 pm## Tanya Khovanova:

Konstantin,

Nice, I know a different one.

22 May 2014, 3:41 pm## Leo:

log(cbrt(8), 8*8)

22 May 2014, 7:01 pm## Leo:

OK, now seriously:

log(sqrt(8)*8)/log(sqrt(sqrt(8)))

22 May 2014, 7:08 pm## Leo:

This works for all digits except 0 and 1, too!

22 May 2014, 7:11 pm