The weights of 4 boxes are 100, 70, 50 and 90 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes and in a combination a box can be used only once?
230
The boxes weigh 100, 70, 50, 90 kg. Check each option as a subset sum (each box used at most once):
310 = 100 + 70 + 50 + 90 (all four). 260 = 100 + 70 + 90. 210 = 70 + 50 + 90.
For 230, no subset works: pairs max at 190; three-box sums are 220, 240, 260, 210; the full sum is 310. So 230 kg is impossible.
Therefore the answer is 230.
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