## MATH PUZZLE # 01

Monday 28 November 2011 at 10:36 pm. Used tags: ,

ARITHMETIC PUZZLE:

using only mathematical  symbols:  =,  +,   -,   x or  * for multiplication,  division n/m,  square root √¯,   exponent ^ or using superscripts,   parens (...),  brackets {...},  iverson brakets [...], the absolute value of n as in |n|,  ≠,  ≤,  ≈,   ≡,  ≥,  factorial or ! of n  or n  all of  which means n x (n-1) x (n-2),....., 1,

and using the four digits:  5,  5,  5,  and 1 , each only once

construct an equation that sums to the number 24

1)    5  x  5   -  1^5  =  24   note   1^5 means the number 1 raised to the 5th power which equals 1

2)    5  x  5   +  (-1)^5  =  24   note: (-1)^5 means the number -1 raised to the 5th power which equals -1

3)     |√¯( 5 X 5 )|  X  5  - 1  =  24  note the √¯ delivers a plus and a minus answer, so use |...| for absolute value.

4)     -|√¯( 5 X 5 )|  X  (-5)  - 1  =  24

5)     5!   /   |√¯( 5  X  5 )|^1  =  24     note factorial 5 = 5! = 5x4x3x2x1

6)     (⌊ | √¯5  | ⌋  +  ⌈ | √¯5  | ⌉)   x    5  -  1   =   24   note that  ⌊   ⌋ and  ⌈   ⌉ means next  lower whole interger and next upper whole interger respectively

7)     (5   -  1/5)   x  5   =   24    note this is probably the most elegant of the solutions

See the List of Mathematical Symbols in Wikipedia: 