Page:Carroll - Tangled Tale.djvu/112

96

Problem.—"There are 5 sacks, of which . 1, 2, weigh 12 lbs.; . 2, 3, 13½ lbs.; . 3, 4, 11½ lbs.; . 4, 5, 8 lbs.; . 1, 3, 5, 16 lbs. Required the weight of each sack."

Answer.—"5½, 6½, 7, 4½, 3½."

The sum of all the weighings, 61 lbs., includes sack. 3 thrice and each other twice. Deducting twice the sum of the 1st and 4th weighings, we get 21 lbs. for thrice. 3, i.e., 7 lbs. for. 3. Hence, the 2nd and 3rd weighings give 6½ lbs., 4½ lbs. for. 2, 4; and hence again, the 1st and 4th weighings give 5½ lbs., 3½ lbs., for. 1, 5.

Ninety-seven answers have been received. Of these, 15 are beyond the reach of discussion, as they give no working. I can but enumerate their names, and I take this opportunity of saying that this is the last time I shall put on record the names of competitors who give no