using 2, 4, 5, 6, 8, 11, and 22 with an answer of 11 and signs of a - b + c X d - e / f - g =11

Question

using the 7 variables listed and order of operations with the computation signs, what is the equation that equals 11?

Answer 1

Rewrite this so that we have positive operations on either side, because all the numbers to be used are positives:

a+cd=11+e/f+b+g. From this we can see that b and g are interchangeable, also that f must be a factor of e.

So e/f=4/2=2, 6/2=3, 8/2=4, 22/2=11, 8/4=2, 22/11=2. Right-hand side (R) minimum is 11+22/11+2+4=19. Maximum is 11+6/2+22+11+8=55. So 19≤R≤55 and similarly 13≤L≤250.

The aim is to get R and L to the same value without repetition of numbers on either side. Because R has the smaller range we need to find out all possible values for R, and we start by grouping according to e/f=2, 3, 4 and 11.

e/f	b+g	R	L
4/2=2	5+6=11	24	110, 187, 250
	5+8=13	26	88, 143, 248
	6+8=14	27	77, 121, 247
	5+11=16	29	60, 140, 182
	6+11=17	30	62, 118, 181
	8+11=19	32	52, 116, 137
	5+22=27	40	59, 74, 94
	6+22=28	41	51, 63, 93
	8+22=30	43	41, 61, 71
	11+22=33	46	38, 46, 53

The first row that has a match of R and L is in bold and so we have a solution, e=4, f=2, b+g=11+22=33, a=6, cd=5*8=40. Note that b and g are interchangeable, as are c and d. There may be other solutions.

One solution out of several: a=6, b=11, c=5, d=8, e=4, f=2, g=22.

CHECK: 6-11+5*8-4/2-22=-5+40-2-22=40-29=11.