119.
The way to arrange 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, so that used once each they form a sum which is equal to 1 is this:—
3570 + 148296 = 1
120.
The sum of the first fifty numbers may be found without any addition thus:—The first fifty numbers form twenty-five pairs of fifty-one each (1 + 50, 2 + 49, etc., etc.), and 51 × 25 is practically 51 × 100 ÷ 4 = 1275.
121.
The tramcar A, which started at the same time as B, but ran into a “lie by” in four minutes, and waited there five minutes till B came along, when they completed their courses at the same moment in opposite directions, could have run the whole distance in ten minutes.