This little jest on the part of Major Trenchard is another trick puzzle,
and the face of the roguish boy on the extreme right, with the figure 9
on his back, showed clearly that he was in the secret, whatever that
secret might be. I have no doubt (bearing in mind the Major's hint as to
the numbers being "properly regarded") that his answer was that depicted
in the illustration, where boy No. 9 stands on his head and so converts
his number into 6. This makes the total 36--an even number--and by making
boys 3 and 4 change places with 7 and 8, we get 1278 and 5346, the
figures of which, in each case, add up to 18. There are just three other
ways in which the boys may be grouped: 1368--2457, 1467--2358, and
2367--1458.