A NEW PASTIME.
ITO THE EDITOR OP THE " SPECTATOR."]
SIB,—Ton may be interested to learn the following facts concerning the new pastime to which reference is made in your issue of December 21st. It appeared some years ago as a question in the mathematical columns of the Educational Times, and was stated thus :—" Write down all the numbers from 1 to 140 by means of four fours. Any arithmetical or algebraic signs may be used, but no other figure. Also do the same with four nines." The question was re-proposed in the early part of 1900, and I endeavoured to solve it. I was successful with the fours in all cases except two, but with the nines I was less fortunate, failing at the time to discover 131, 133, 137, 139. Shortly afterwards a question appeared under my name, asking for the missing numbers. Several solutions were forwarded to me by correspondents. None, however, were satisfactory, for they involved higher algebraic "notation," such as the Gamma function, and this opened out an interesting question as to the distinction between " sign" and " notation," and how precisely we were to limit the term " algebraic." This difficulty may be avoided by restricting the question to " arithmetic or elementary algebraic signs," and we should thus be allowed to use the sign for factorial, perhaps also the notation for permutations. The figures 4 and 9 are chosen because their square roots are integral. I have since found all the numbers, with the exception of 133, in the four nines.—I am, Sir, &c.,
T. G. Wiwoms, S.J. St. Bean's College, St. Asaph, N.W.
[We print the above letter out of a sheaf received on the subject, as the best answer to the question put by several of the writers,—What "signs " are permissible P Three writers have sent complete lists up to 100, and one sends a formula which carries him as far as 331. We can publish no more letters on the subject.—En. Spectator.]
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