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Maths Challenge - A Little Teaser!

Started by admin, October 03, 2011, 11:20:10 pm

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Math Challenge:
A little Teaser

(U3A Members can obtain the solution by downloading the attachment below)

Census man:    "Good morning sir , I've come to check the details on your census form, It appears you have three children, but you have neglected to give their ages."
Householder:-  "An oversight on my part sir, but since you are clearly a mathematician, I will tell you that  the product of their ages is 36, and  the sum of their ages is the same as the number on the gatepost there. You will then have all the information that you require."

"Sadly no!"  said the Census man after only a brief pause for thought.  "That is not sufficient information."  (His mind was razor-sharp, a mathematician of the first order, and he could recognise a smart-Alec when he met one.)

"Oh silly me"  said the householder.  "Of course you are right; I should have mentioned, that is my eldest you can hear playing the piano."

The census man thanked the householder and correctly filled in his form. 

Can you too, work out the ages of the children and the number on the gatepost?


peter hall

Hi ,
Sorry I'm being dim here. How do we know what the number on the gate is?


This is perhaps as much logic as maths - you just need some paper and a pen.


November 17, 2011, 11:06:17 am #3 Last Edit: November 17, 2011, 11:15:56 am by Arturo
Yes Pete here is the logic.   There are only eight combinations of three ages that can give a product of 36.  Namely 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.   Looking at the corresponding sums of their ages we get 38, 21,16,14,13,13,11,10.  If the number on the gate post is ,say, 14 then the children must be 9-4-1.No problem!  The only problem arises when the sum and hence the number on the gatepost is 13 which can be either 9-2-2 or 6-6-1. Which is why the C.M. has to ask for more information.  Since the householder then refers to an eldest child rather than "one of my twins" it must be the 9-2-2 arrangement.  Hope this clears things up!