How do you add, subtract, multiply and divide 3, 5, 7, 8, 25, 75 to get 127?
This time I'm showing how I reason to find a solution.
First I thought that 127 is close enough to 125, so 5 x 25 = 125, need to add 2. Getting 2 out of 3, 7, 8, 75 was simple: 2 = 7 + 3 - 8. Hence 127 = 5 x 25 + 7 + 3 - 8.
Another thing I would try is adding 75 and 25 to get 100. Then it's a matter of getting 27 out of 3, 5, 7, 8. That's not so difficult. 27 = 5 x 7 - 8. Hence 127 = 75 + 25 + 5 x 7 - 8 = 100 + 35 - 8.
The NumberWiz game gave this solution: 127 = 5 x 3 x 8 + 7 = 15 x 8 + 7. Elegant.
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