NumberWiz example with solution-reasoning, Tuesday

How do you add, subtract, multiply and divide 1, 7, 7, 10, 25, 100 to get 208 ?


The first thing I wanted to try was 108 + 100. However getting 108 out of 1, 7, 7, 10, 25 seems difficult. Other similar combinations don't look good either: 101 + 107 or 110 + 98 or 125 + 83. Using 100 does not look promising enough.


250 (10 x 25) seems a better starting point. We need to subtract 42, and now a solution comes to mind: 208 = 250 - (7 - 1) x 7. Solved!


But how about (7 + 1) x 25 ? We must get 8 out of 7, 10, 100. Impossible.


Try 7 x 7 x 100 / 25 = 196. We need another 12, but we can only make 11.


Try (7 x 7 + 1) x 100 / 25. We need to make 8 out of 7, 10. Impossible.


The NumberWiz game takes the 250 route as above. It seems the only solution.