# Five of these numbers

rgoudie
Posers and Puzzles 27 Jun '04 22:32
1. 27 Jun '04 22:32
Five of these pseudo-numbers interact together to give the number 1 as a solution.

Which five numbers and in which order?

+19 x9 +29 x7 -999
-94 +173 +65 -236 x8
+122 x5 x212 +577 -567
+190 x6 x4 -435 x22
x13 -87 x12 -172 +177

-Ray.
2. 10 Jul '04 16:04
There are 3 solutions with no multiplication:
-236 -94 +19 +122 +190
-236 -87 +29 +122 +173
-172 -94 +29 +65 +173

There is 1 solution involving a repeated multiplication added to two numbers:
-435 -172 +19 x4 x8

There is 1 solution involving a repeated multiplication added to a product:
-567 x9 +29 x8 x22

There are 8 solutions involving two products:
-999 +65 x6 +122 x5
-567 -94 x5 +173 x6
-435 x8 +19 +577 x6
-236 -172 x12 +177 x13
-236 -87 x4 +65 x9
-172 x7 +65 +190 x6
-172 x8 -87 +122 x12
-172 x9 +29 +190 x8

There are 11 solutions involving one product:
-999 -435 +19 +177 x8
-999 -236 -94 +190 x7
-567 -435 -236 +177 x7
-567 -236 -172 +122 x8
-567 +19 +29 +65 x8
-435 -236 +19 x5 +577
-236 -172 +19 +65 x6
-236 -172 +29 x8 +177
-236 -94 -87 +19 x22
-172 -94 +29 x5 +122
-94 x4 +65 +122 +190

Altogether there are 24 different solutions.
3. 10 Jul '04 16:46
Please, tell me that you wrote a neat little computer program to generate these solutions by brute force, and that you did not spend time doing them by hand.

-Ray.
4. 11 Jul '04 11:42
I used an Excel macro ðŸ™‚
5. 11 Jul '04 20:24
Originally posted by garethn
I used an Excel macro ðŸ™‚
Good work.

It pains me to imagine you sitting under a low-wattage light, in the middle of the night, with pen and paper, writing out every permutation and determining whether it results in 1. ðŸ™‚

-Ray.