135.
Three horses, A B C, can be placed after a race in thirteen different ways, thus:—A B C, A C B, B A C, B C A, C A B, C B A, or A B C as a dead heat; or A B, A C, or B C equal for the first place; or A first with B C equal seconds; or B first with A C equal seconds; or C first with A B equal seconds.
136.
The 34 points scored against Oxbridge by the New Zealanders can be made up in two ways, either by 8 tries and 2 converted tries, or by 3 tries and 5 converted tries.
The highest possible score on these lines is 10 tries converted, equalling 50 points, and as the New Zealanders’ score, if all tries are converted, becomes four-fifths of this, their actual score was 3 tries and 5 converted into goals.
137.
The smallest number, of which the alternate figures are cyphers, which is divisible by 9 and by 11 is 909090909090909090909!