Now if I attempted, following the example of Mr. Dallas, to interpret the problem, would it not be quite common sense to argue as follows:
By the agreement the players intended that all except the highest winner should be losers. Therefore the winners D, E and F must be made losers, and in fairness should only be considered losers of the smallest number of points which a player can lose, which is one point. In that case D, Eand F would have to pay $0.17c. each. By making D E and F losers in the above-suggested manner, all the five players are brought into a common category, and why should my method be more objected to, than Mr. Dallas'?
4.—Mr. Dallas remarks: "If disrogardig everything but the scores of the five contributors we apply to them the strict mathematical doctrine of proportions we arrive at a result which is certainly not in accordance with the clause that sti-plates that all five contributors shall y."" Quite right, and therefore a correct solution of the problem is impossible. For according to the terms of the problem everything but the scores of the five contributors must be disregarded. By commencing his quite correct statement ith the words "if disregarding everything but the scores of the five contributors. Mr. Dallas seems to imply that this " disregarding, etc." is wrong. At least some readers might think so. Therefore I consider it necessary to point out that there is nothing to regard except the score of the five players, and that these, if any correct solution is to be arrived at, must be treated, according to the strict mathematical doctrine of proportions. If the result does not agree with other requirements of the problem, it follows that the problem is, and that a correct solution is impossible, just as it is impossible to correctly solve the problem of constructing a triangle with four sides.
Tftherefore Mr. Dallas with-the words "'and we must look for some other solution," means to say that he wants to find a correct solution of a problem which, as he himself has just demonstrated cannot correctly solved, because it imply ities, he evidently has argued himself into acleer contradiction. And what else can we suppose Mr.. Dallas meant by the word "solution," if not a.correct solution? amind is this."Tho problem as it i yon What appears to have been in his (in its ordinary grammatical sense), does admit of woarrect solution, thotefore we must try to find another sense. But in so doing the original problem is of course changed into a quite different one, and Ihave shown (under 3) that if it is allowable to introduce another sense into the problem, the sense suggested by Mr. Dallas is not the only possible ove.
If Mr. Dallas had said '*we must look for some other problem" instead of solution, that would be in accordance with his further proceedings. These consist simply in trying to convince the reader that the problem is not the problem which was published, but another one which was not fave been understood and intended by at published, and which certainly cannot
agreement, The problem which Mr. Dallas least one of the six players who made the solves is so extremely simple,. that it is impossible to conceive, that, if understood intended by all the six players, any dispute could have arisen.
An absolutely correct solution being impossible, what then isto be done? I see nothing but a compromise possible, if the $30 are to be actually paid, But this compromise ought not to be called a correct solution. My view is that it would be fair to treat D, E and F somewhat better than would have been the case if the score had. been A+175, B-168, C-4, D-1, E-1, F-1, and each player paying in the pr portion of lis score the amount in question is so small that the players no doubt will easily agree amongst themselves, [We publish this letter, from a correspondent at a distance, as it was written before our intimation that the subject was closed in our columns had reached him,—Ev.]
Text read from the printed page and cleaned; old type leaves the occasional error.