Using only two 2s and any of the standard mathematical symbols, write an expression whose value is equal to 5.

An approach could be: sqrt((2 * 2)!) = 4.90

Standard mathematical symbols (for this problem) are: addition, subtraction, multiplication, division, exponentiation, square root, factorization, parenthesis, positive, negative, ln, log. Superfactorials and such are not excluded, but not part of the desired solution. Any symbol having a value of its own, such as e, pi, and infinity, is not authorized.

The following is a partial list of solutions, of which the first two listed do not require either the CEILING or FLOOR function (the second, though, uses the undesired primorial and subfactorial):

1. SQRT(.2^-2)
2. p₂# - !2
3. CEILING(SQRT(22))
4. CEILING(TAN(2)²)
5. CEILING(SIN(2)/.2)
6. SQRT(CEILING(ARCSIN(.2))^-2)
7. SQRT(CEILING(SQRT((!(2+2))!))
8. SQRT(CEILING(SQRT((!(2*2))!))
9. SQRT(CEILING(SQRT((!(2²))!))
10. CEILING(SQRT(SQRT((2+2)$))
11. CEILING(SQRT(SQRT((2*2)$))
12. CEILING(SQRT(SQRT((2²)$))
13. CEILING(CSC(2^-2))
14. FLOOR(COS(2)^-2)
15. FLOOR(SEC²(2))
16. FLOOR(LN(2.E+2))
17. FLOOR(SQRT(SQRT(<2>₂)))

Edited on September 17, 2008, 12:39 am

Posted by Dej Mar on 2008-09-16 11:16:02