Problem.—To mark pictures, giving 3 ×'s to 2 or 3, 2 to 4 or 5, and 1 to 9 or 10; also giving 3 o's to 1 or 2, 2 to 3 or 4 and 1 to 8 or 9; so as to mark the smallest possible number of pictures, and to give them the largest possible number of marks.

Answer.—10 pictures; 29 marks; arranged thus:—

Solution.—By giving all the ×'s possible, putting into brackets the optional ones, we get 10 pictures marked thus:—

By then assigning o's in the same way, beginning at the other end, we get 9 pictures marked thus:—

All we have now to do is to run these two wedges