PRIZE PUZZLE FOR MAY 2006
WHAT DAY WAS IT?A mother has three children who were all born on a Friday. She was interested in the ages of her children in days and liked to do the calculations from time to time. On one particular day she made a remarkable discovery: the sum of her children's ages was exactly the same as her own age in days. She was born on a Thursday. What day of the week did she make this discovery?
The method of solution to this problem is to realise that we are only dealing with modulo 7 arithmetic; that is; the remainders after dividing by 7 which are numbers in the range 0 to 6. The mother has ages 0,1,2,3,4,5,6 from Thursday to the next Wednesday respectively whereas the sum of the three children's ages increment by 3 for each day of the week. Friday is zero. We then have the sequence Saturday 3; Sunday 6; Monday 2; Tuesday 5; Wednesday 1; Thursday 4; Friday 0 again, adding three each time and casting out anything above or equal to 7. The Mother's sequence of modulo 7 ages shows that Tuesday is age 5 and this is the answer: Tuesday, since both sequences of ages are the same on Tuesday.
I received four answers. They were from John Stafford, Colin Rowe, Gwynn White and Clem Robertson. Gwynn White won the draw and the £5 book token.