Answer to January 2014 Problem of the Month

James Alarie insisted that we do this problem again this year:

Write expressions for all the numbers from 1 to 100 using only the digits in the current year in order and using the operations +, -, x, ÷ (or / for divided by), ^ (raised to a power), sqrt (square root), ! (factorial), and int (or [ ] for greatest integer function), along with grouping symbols.

So, the first problem of the new year is to use only the digits 2, 0, 1, 4, (and in that order) along with the operations listed above to write expressions for all the numbers from 0 to 21.

Extra credit for those who can go past 21 (consecutively).

Some Solutions to the Problem:

0 = 2 * 0 * 1 * 4
1 = 2 * 0 + 1^4 or -2 + 0 -1 + 4
2 = 2 + 0 * 1 * 4
3 = 2 * 0 - 1 + 4
4 = 2 * 0 * 1 + 4
5 = 2 * 0 + 1 + 4 or 2 + 0 - 1 + 4
6 = 20-14 or 2 + 0! -1 + 4
or 2 + 0 * 1 + 4
7 = 2 + 0 + 1 + 4
8 = 2 * 0! * 1 * 4 or 2 + 0! + 1 + 4
or (2+0(1))4
9 = (2 + 0!)*(-1 + 4) or (2 + 0!)! - 1 + 4
or (2+0+1)^sqrt(4)
10 = 2 * 0!*(1 + 4) or (2 + 0!)! * 1 + 4
or (2+0)(1+4)
11 = (2 + 0!)! + 1 + 4
or sqrt(2^0+(1+4)!)
12 = (2 + 0 + 1) * 4
13 = -(2^0) + 14 or -2 + 0! + 14
14 = 2 * 0 + 14 or (2^0)(14)
15 = 2^0 + 14 or (2 + 0!) * (1 + 4)
or 20-1-4
16 = 2 + 0 + 14 or (2 + 0! + 1) * 4
or 20-1(4)
17 = 20 + 1 - 4 or 2 + 0! + 14
18 = 20 - sqrt(1 * 4) or -(2 + 0!)! * 1 * 4!
or 20-1(sqrt(4))
19 = 20 - (1^4) or 20 - 1 ^ 4
20 = 20 * (1^4) or (2 + 0!)! + 14
21 = 20 + (1^4) or -(2+0+1)+4!
22 = 20 + 1 * sqrt(4) or -2 + 0 * 1 + 4!
23 = 20 - 1 + 4 or 2 * 0 - 1 + 4!
24 = 20 * 1 + 4 or 2 * 0 * 1 + 4!
25 = 20 + 1 + 4 or 2 * 0 + 1 + 4!
26 = (2 + 0! + 1)! + sqrt(4)
or 2 + 0 * 1 + 4!
27 = 2 + 0 + 1 + 4! or
int(sqrt(((2 + 0 + 1)!)!) * sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(4))))))))
28 = 2 + 0! + 1 + 4! or ((2 + 0!)! + 1) * 4
29 = (2 + 0!)! - 1 + 4!
or int(sqrt(((2 + 0 + 1)!)!) * sqrt(sqrt(sqrt(sqrt(4)))))
30 = (2 + 0!)!*(1 + 4)
or (2 + 0 + 1)! + 4!
31 = (2 + 0!)! + 1 + 4!
32 = 2 * ((0! + 1) ^ 4) or 2^(0+1+4)
33 = [(sqrt(2) + 0 * 1) * 4!]
34 = 20 + 14
35 = [sqrt(((2 + 0!)! + 1)! )/sqrt(4)]
36 = (2 + 0!)! * (-1 + 4)! or
37 = [sqrt(sqrt(2) + 0 + 1) * 4!]
38 = (20 - 1) * sqrt(4)
39 = [2 + 0 +sqrt(sqrt(sqrt(sqrt((1 + 4!)!))))]
40 = 20 * 1 * sqrt(4)
41 = [sqrt(sqrt(sqrt(sqrt((2+0!)!*(1+4!)!))))]
42 = (20 + 1) * sqrt(4)
43 = (2 +0!)! + [sqrt(sqrt(sqrt(sqrt((1 + 4!)!))))] or 20-(1-4!)
44 = 2 * (-0! - 1 + 4!) or 20+1(4!)
45 = -[sqrt(2)] + [sqrt(sqrt(sqrt(sqrt((0! + 1 + 4!)!))))]
46 = 2 * (0 - 1 + 4!)
47 = -[sqrt(2)] + (0! + 1) * 4!
48 = 2 * (0! - 1 + 4!) or (2+0(1))!4!
49 = [sqrt(2)] + (0! + 1) * 4!
50 = 2 * (0 + 1 + 4!)

James Alarie gets extra credit for solving 1 through 50.

1. James Alarie	Flint, Michigan
2. Lisa Merwin, J. Bechto, M. Myers	Taylor, Michigan

January 2014 Problem of the Month

Correctly solved by:

January 2014
Problem of the Month