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 22 + 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.

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7 Comments

  1. George R.:

    Well, I’ll try the easy ones first 🙂
    6*(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.

  2. Tanya Khovanova:

    George, that was fast. One more to go.

  3. Konstantin Knop:

    8 – sqrt(sqrt(8+8))

  4. Tanya Khovanova:

    Konstantin,

    Nice, I know a different one.

  5. Leo:

    log(cbrt(8), 8*8)

  6. Leo:

    OK, now seriously:

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

  7. Leo:

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

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