Monthly Brainteaser and Decembers AnswerWednesday, January 5th, 2011
Last month’s nice little problem was this:
The busy housewife had just had an argument on the phone with the local council about an issue with one of her stepchildren when there was a knock on the door. On the doorstep stood a man with a clipboard. “I’m from the Council” he said, “and I am doing a survey for the Social Services Department. Can you tell me, please, how many children you have?” “Three” she replied curtly. “And how old are they?” asked the man. Feeling somewhat peeved about anything to do with the council, the woman replied “Well, if you multiply their ages together, the result is 36”. “Hmm” muttered the man with the clipboard, “But that doesn’t give me much to go on”. The woman thought, then said “If you add their ages together, the total is the number of the house next door”. The man jumped over the low wall to look at the front door of the adjacent house, jumped back, and said “Can you give me just one more bit of information, please?” “My eldest was born in January” snapped the woman, and slammed the door in the man’s face. But he wasn’t bothered. He just wrote down the correct ages of the three children and moved on to make his next call.
How did he work out the ages? All the information is there. But treat all ages as whole numbers, for example don’t use fractions of a year and twins would be exactly the same age as each other. You just need to sit down with a pencil and paper and work through the problem step by step.
This really is not as difficult as it looks provided you take your time, work things out in sequence as did the man with the clipboard, and do not complain about insufficient information.
We know that there are 3 children, and there only 8 combinations of ages that, multiplied together, come to 36 (Ask yourself what numbers divide into 36). They are: 36.1.1; 18.2.1; 12.3.1; 9.4.1; 9.2.2; 6.6.1; 6.3.2; and 4.3.3. Check it out yourself! However the man could not tell which combination of ages was correct, so he asked for a second clue. By adding the ages together he arrived respectively at 38; 21; 16; 14; 13; 13; 11; and 10. By looking at the number of the house next door he hoped to determine which of these it was, and indeed had it been 38, 21, 16, 14, 11 or 10 he would have had his answer. However since the jump over the wall did not give him the answer, the number must have been 13 because there are two combinations that produce this number. The third bit of evidence was that the eldest child was born in January. Actually the month of birth is immaterial, what is important is that the woman referred to “my eldest”. Had the ages been 6.6.1, there would not have been an eldest, but rather two older. Therefore the children’s ages were 9, 2 and 2.
Now, in view of the work you have to do as a result of reading the first item in this newsletter, a simple question for you this month:
If you overtake the third person in a race, what position are you now in?
Answer next month.