A Problem:
Can Readers Solve It?
To the Editor of the "Nown-Cixa Dany News" si The following problem from *Eequire's" February issue has great deal of discussion and nents, which unfortunately have not helped to solve ite It isa Tosical problem and has a perfectly good Tywoukd be much obliged if you would be good enough to challenge the masterminds amongst' the read~ of Your correspondence column.
John sad to his cider sister Mary, ettled any "age an monte "stay hetare "Thankaeseine, day? of ne week as Mary Shanghai, Apr. 15, A Reader's Solution To the Editor of the "Nonni-Cuaxa Dany News" worded, so that it is with some dif dence that 1 submit that if Mary was om in a Jeap year or the following year, she was also born ona Sun= Gay otherwise on a Saturday.
'The key to the problem lies in' the relationship 10 (8 +m johns "age" Wy ments tein days exeeedea hi its by'an even number months, m years 9g0 number of John's summers.
Fears "ano. Ste is evidently @ multiple of 10; not tougher than' Gi singe John seat most seven' years Now if the word "months" refers to calendar months, it may. easily be shown that a lifetime of Int months from November gives John a number of summers which in no case permits to exceed 1. But John would be one calendar month oid at an age of 80 days, which does not exceed. his Axe In months by an even number; hence the problem would appear to have no solution, "If however "months" means lunar months of 28 days, we find that it M=60, 70 oF 80, the number of John's (completed) simmers. is. sich that m=2. (In this ease, John would be two lunar months old at an age of 56 days, which does" exceed "his age in months by, an even number.)
But if John's present aye is at most seven, he cannot have been 70 oF 60 months old we years ayo: hence: 'M=00, and the present number of John's! summers is 6, Now John was born on a Sunday. Sixty lunar months later it is again course Sunday, and the same date two years Inter is Mary's eighth birthday, which will therefore be a Wednesday or a Tuesday according to whether a leap year does or does not intervene, The date of Mary's birth, eight years previously, must accord: ingly have been a Sunday oF a Satur-
To take two conerete examples. If John was born on Sunday, November 20, 1998, sixty lunar months brings to June 27 1943, and the day' of Mary's birth—June 27" 1007—Was a Sunday.
But it John was born on Sunday November 22, 1990, sixty lunar months brings us {o June 39 1941, and the day of Mary's birth—June 29 1995—was a Saturday.
Tneldentally, i¢ of your readers wish to take' their minds off world affairs by exercising them on prob-Jems, T know of none better than the old "lassie of the black and white labels. For those not familiar with T repeat the tale as it was told to 'A judge had condemned three felons to hang, but he decided to give them all a chance to save their lives "Here in this box." he said, "E have three black labels and two white ones, and I shall pin one label on the tack of each of you, s0 that you can each see the colour of the label on the other two, but not the label on your own buck. To the one who first tells me the colour of his own label, and satisfactory reasoning. therefore, I Will xive a free pardon."
So the judge picked three labels at Fandom, and pined ne on the back of each man.
The three men studied exch others! labels for some. considerable time without being sable colour of their own, wher them, ha alized what the colour ut must be, What was the colour of his libel, and how did he know The problem is simply one reasoning there is no catch in Shanghai, Apr. 35, EDITOR (continued)
Text read from the printed page and cleaned; old type leaves the occasional error.