David,

To avoid spoilers, I’ve sent you an email with some suggested solutions. Neat!

Best,

Peter

Peter Gallaghers last blog post..Chroming the Internet

Cool and well done. Not the only solutions, so I will post all the answers sent in tomorrow. Cheers

I’ll wait for the solutions I have one for all except the first and am going to give up on it.

I think the solutions to 3,4,5,6,7,8 and 9 are fairly straightforward. However, number 1 isn’t.
I’ve tried to reproduce it below, the right hand side should read “the infinite root of 6″.

1 x 1 x 1 = ∞√6

carl

1*1*1 = 6^0 did cross the mind but I thought it might not be legit.

φ(n) (Euler’s totient function) is your friend…

Are other digits allowed as subscripts or superscripts?

If you’re thinking Euler (or Boltzmanm, Planck or Avagadro for that matter) your friend may really be the Magic Number Machine.

Peter Gallaghers last blog post..Precautionary principle, misleading and undemocratic

Damn… Try that link again: Magic Number Machine

Peter Gallaghers last blog post..Precautionary principle, misleading and undemocratic

Bob D: Yes.
Jan: 6^0 Works for me

Thanks David,

for both the fun and the answer.

I wasn’t sure whether we we could operate on both sides.

Now I’m really curious about what Josh might be thinking. Josh?

φ(3+3+3) =6
φ(6+6+6) =6

But are you ready for my answer?

David

Ahah.

I am are others?

OK: Where n is any number:

(n^0 + n^0 + n^0)! = 6

I’ll collate all the answers into a post if you want to surrender them now.

David Stockwells last blog post..A maths home work quiz

1! × ⌊tan 1⌋ + log 1 = ⌈cos 6⌉

☺

Good mathematicians start conversations either by drawing a triple integral first, or by explaining “On one hand….”

Digital solutions:

On one hand I found 5 fingers + 1 thumb = 6.

On the other hand, I found 4 fingers + 1 thumb = 5.

(Noted asymmetry and mirroring).

While looking for a nice solution in hand, I deduced that people smart enough to know about Euler’s Totient Function are w…….s. (wiki readers).

Time for solution = 0.3 milliseconds.

(This has not been peer reviewed).

(1+1+1)!=6

More serious this time, does this fit the rules of the game? Might not work for n = 0.

{[(n)! – (n-1)!]/3 + [(n)! – (n-1)!]/3 + [(n)! – (n-1)!]/3 } = n

I have never really thought about the sign of the factorial of a negative integer. I guess it alternates.

Thought time: 2 weeks