October 2020
Problem of the Month
Five Digits
Submitted by Brijesh Dave
Can you arrange the five digits, 1, 2, 3, 4, and 5 in such a way that,
with the aid of some mathematical symbols, you can obtain the four numbers: 111, 222, 333,
and 999?
You must use each of the five digits exactly once but in any order.
You may use any of the math symbols or functions:
addition (+), subtraction (-), multiplication (x), division (/), exponentiation (^), factorials (!), and parentheses ().
Solution to the Problem:
111 = 135 - 24 or
111 = (1*5!)-(2+3+4) or
111 = 54 * 2 + 3* 1
or
111 = 1(23 * 5 - 4) or
111 = (2^5 + 4 + 1) * 3
or
111 = 5! - 3! - 4 + 2 - 1 or
111 = 5! - (3^2) * 1^4
222 = 213 + 4 + 5 or
222 = ((5+1)^3)+(4+2) or
222 = 15 ^(4/2) - 3
or
222 = 3^(5) - 4! + 2 + 1 or
222 = (2^5 + 4 + 1) * 3!
333 = 345 - 12 or
333 = ((4x2)! / 5!) - (3*1) or
333 = ((3!)! - 54) / 2 * 1
or
333 = 5! * 3 - 4! - 2 - 1
999 = 4 ^ (3! - 1) - 25 or
999 = 5^3 x 4 x 2 - 1 or
999 = ((5x2)^3)-(1^4)
or
999 = (5^3 * 2 *4) - 1 or
999 = (5*4/2)^3 - 1
or
999 = (3!-2)^(5) -4! - 1