permute _ Editorial

My friend Mike just sent me a text message, asking if I can think of a way to
make the numbers 10, 10, 9, 9, and 1 equal 8. He says I am only allowed to use
addition, subtraction, and/or multiplication (+, -, *), and numbers must be used
the number of times they are listed (i.e., I should use 1 once, but I should use
10 and 9 both twice).

I solved this problem myself, and I kind of lucked out, because there was a
solution. It turns out that (((10 - 10) * 9) + (9 - 1)) = 8, but I’d like to be
able to know in the future whether or not a solution even exists first, for if
Mike texts me again. Can you help?

You need to write a program that takes a list of numbers and a target result
and outputs whether or not it’s possible to combine those numbers using only
addition, subtraction, and/or multiplication to get the target result.

You will first receive a line that says how many problems your program can
expect, N, followed by N lines of an arbitrary amount of integers. The last
integer on each line is the target. If a combination can be made, output “Y”,
otherwise output “N”.



10 10 9 9 1 8