The home work quiz

OK, here are the solutions I received to the home work quiz. Thanks to Alan D. McIntire, Peter Gallagher, Jan Pompe, BobD and Josh for contributions.

1:
(1+1+1)!=6
1*1*1 = 6^0
1 x 1 x 1 = ∞√6
11|4 + 1 = 6 where the 4 is a subscript indicating “base 4″
1×1+1 = φ(6)
2:
(2*2) – 2 = 6
2 + 2 + 2 = 6
3:
(3*3) – 3 = 6
φ(3+3+3) =6
4:
4^(1/2) + 4^(1/2) + 4^(1/2) = 6
4 + 4 – 4^(1/2) = 6
5:
(5/5) + 5 = 6
5 + 5 / 5 = 6
6:
6+6-6=6
6 – 6 + 6 = 6
φ(6+6+6) =6
7:
7 – (7/7) = 6
8:
8-8^0-8^0 = 6
8^(1/3) + 8^(1/3) + 8^(1/3) = 6
8 – (8+8)^.25 = 6
Γ(8 -8/8) = 6!
9:
(9 + 9) / 9^ (1/2) = 6
9^(1/2) x 9^(1/2) – 9^(1/2) = 6
9 – (9 / 9^.5) = 6

φ is Euler’s Totient Function.
Γ is the Gamma function.

And my solution where n is any number:
(n^0 + n^0 + n^0)! = 6

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0 thoughts on “The home work quiz

  1. A couple of others:
    1:
    11|4 + 1 = 6 where the 4 is a subscript indicating “base 4”

    4:
    4 + 4 – 4^(1/2) = 6

    By the way:
    4! / 4 = 6
    is true but lacks a 4.

  2. A couple of others:
    1:
    11|4 + 1 = 6 where the 4 is a subscript indicating “base 4”

    4:
    4 + 4 – 4^(1/2) = 6

    By the way:
    4! / 4 = 6
    is true but lacks a 4.

  3. I think solutions like

    8 – (8+8)^.25 = 6

    and

    (9 + 9) / 9^ (1/2) = 6

    are cheating because of those additional numbers, 0.25 and 1/2.

    Why are ^0.25 and ^ 1/2
    allowed, and not -21, resulting in trivial solutions
    like 9+9+9 -21 =6 .

    You could have gotten around it by throwing in SQRT(SQRT) and SQRT.

    My own solution to 8 was
    Gamma (8 -8/8) = 6!

    I couldn’t solve the 9 series without the
    SQRT.

  4. I think solutions like

    8 – (8+8)^.25 = 6

    and

    (9 + 9) / 9^ (1/2) = 6

    are cheating because of those additional numbers, 0.25 and 1/2.

    Why are ^0.25 and ^ 1/2
    allowed, and not -21, resulting in trivial solutions
    like 9+9+9 -21 =6 .

    You could have gotten around it by throwing in SQRT(SQRT) and SQRT.

    My own solution to 8 was
    Gamma (8 -8/8) = 6!

    I couldn’t solve the 9 series without the
    SQRT.

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