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Zag · Tired of his old title

This is from the IBM Research Puzzle site, the challenge for January 2010. I rather liked it, primarily because I found it challenging but I managed to solve it.

Present a computation whose result is 5, being a composition of commonly used mathematical functions and field operators (anything from simple addition to hyperbolic arc-tangent functions will do), but using only two constants, both of them 2.

It is too easy to do it using round, floor, or ceiling functions, so we do not allow them.

Update 1/11: You can only use 2 instances of the constant 2, so solutions like (2+2+2/2) is illegal. You can not use variables so (x+x+x+x+x)/x is not allowed. You can use square root and power, but squaring will cost you one "2" and other constant powers are not allowed.

lostdummy · Daedalian Member

I'm sure this is not intended answer, but when I saw "hyperbolic arc-tangent..." I couldn't resist:

StrToInt( BinToStr(2) ) /2

this use functions that I consider more "common" that above mentioned hyper-arc-xyz ;)

Zag · Tired of his old title

You should submit that. It might be original, unlike mine.

For anyone wanting to solve it with trig functions, think of right triangles, and the Indian chief SOHCAHTOA.

JDTAY · obseletes now

I have an answer, but it involves the number 1984.
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Antrax · ESL Student

I really like lostdummy's answer. In C you could simply do: sqrt('2' / 2) which is similar but feels less cheaty.
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milkshake · Daedalian Member

Does T ₂ + 2 count? ^^

(Edit: That's T sub 2. It didn't show up right at first.)

Chuck · Daedalian Member

In shoe sizes an underline means add ½ to the number so it would be 2 × 2. The underline is a commonly used notation.

Trojan Horse · Daedalian Member

Zag · Tired of his old title

Yep. That's what I had, though, in order to be original, I also submitted this:

(sec(arctan(2!!!!!!!!!!)) ^ (2!!!!!!!!!!!!!!!)

Ph.D. in math, eh? I only managed a BSEE, and that was 26 years ago.

PuzzleScot · Daedalian Member

Before the ammendum was added regarding variables, I submitted:

5 = sum(n<=2,n € Z) n^2

[Sum of square of integers <=2. ie, 1^2 + 2^2 = 5]

DevJoe told me he'd submitted this:

Zag · Tired of his old title

bonanova · Daedalian Member

Suggested by a colleague: lb(2/(lb(sqrt(sqrt(sqrt(sqrt(2)))))))
I had not heard of the lb notation, but he assures it's of common use in information theory.
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Trojan Horse · Daedalian Member

I'm assuming "lb" is not an abbreviation for "pound". I've never seen that symbol used like this before.

bonanova · Daedalian Member

I hadn't, either. But I found this ...

http://en.wikipedia.org/wiki/Binary_logarithm

Different solution from same person: cosh(arcsinh(2))^2
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