# A Fairly Simple Equation #2

I got a lot of positive feedback on my last puzzle, A Fairly Simple Equation (even though it was apparently a lot easier than I thought it would be!) So, I've got another similar puzzle.

General Rules (Updated):

1. You must insert the given numbers into the given equation, each number replacing a letter in the equation, to get the given output.

2. You may not combine, invert, or reverse numbers. This doesn't have the lateral thinking tag for a reason.

3. Parentheses, or a number and parentheses, mean multiplication if they're put together like this: $$(A+B)(C-D)$$ or this $$A(B+C)$$

4. Rounding to the nearest whole number is allowed unless stated otherwise.

5. Reversal of the order of the numbers in an addition or multiplication is not counted as a separate answer. $$(2+3)*4$$ and $$(3+2)*4$$ are considered the same solution, for example.

6. The Order of Operations applies.

Specific #2 Rules:

1. The given numbers are, for this puzzle, $$2, 3, 4, 5, 6, 7, 8, 9,$$ and $$11$$.
2. Two of the given numbers will not be used.
3. The given output is $$102$$.
4. I could only find one answer, although it's definitely possible there may be more.

The Equation: $$(A*(B+(C+D)*E))/(F/G)$$

Good Luck!

• Make sure to accept an answer if you think it is correct :) – Quintec Sep 24 '18 at 17:35
• To be extremely pedantic, it's not an equation but is an expression, since there's no equals sign to equate anything. – Harfatum Sep 24 '18 at 22:56

I found one:

2 3 6 5 9 8 4 for A-G respectively.

Strategy:

I got a bit lucky. I set A=2 and F and G equal to 6 and 3, and then 8 and 4, so that they would cancel out and I had a simpler problem to solve. From there it was some simple guess-an-check to get the inner expression to equal 102.

I made a little python program to find them all, there are a total of 64 solutions. The first one is

2 3 4 9 5 8 6 for A-G respectively

for a,b,c,d,e,f,g in itertools.permutations((2,3,4,5,6,7,8,9,11), 7):
if -0.01 < (a*(b+(c+d)*e))/(f/g) - 102 < 0.01:
print(a,b,c,d,e,f,g)

• ... the tag says no-computers... – Jason Kim Sep 22 '18 at 5:09