Maths Puzzle :: Discussion
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A toy vendor is selling toys from door to door. He visits a house & asks the owner lady to buy toys for her kids. Lady, being a smart customer, says to Toy Vendor If you can tell me the ages of my 3 Kids correctly then only I will buy Toys from you.
Toy Vendor says OK am, Please give me some clue If you multiply ages of my 3 kids you get figure 36. And if you add ages of my 3 kids you get House Number of my neighbor replies Lady.
Toy Vendor thinks for a while, goes & notes Number of Neighbour's house & returns saying am, some more information is required
OK, my eldest daughter plays Harmonium very nicely replies Lady. Oh, in that case, I have got the answer to your question replies Toy Vendor & tells the Lady the correct ages of her Kids.
Can you tell ages of Lady's Kids? What is House Number of Lady's Neighbour ??
Explanation :
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There are a few sets of three numbers that multiply to 36. There must be more than one of these that sum to the house number, otherwise, the toy man would know the ages. However, there must be only one of these that has a single maximum value ("eldest") since the toy man is then able to work out the ages.
Presumably, the ages are represented by integers (whole numbers) otherwise there are many other possibilities; eg. 0.5, 4.5, 16.
The following sets of triples multiply to 36. Their sum is in the 4th column
1 1 36 38
1 2 18 21
1 3 12 16
1 4 9 14
1 6 6 13
2 2 9 13
2 3 6 11
3 3 4 10
The only ones that sum to the same number are (1,6,6) and (2,2,9) so the neighbor's house number must be 13.
The harmonium-playing eldest daughter must be 9 (unless we allow for the mother identifying a first-born 6-year-old twin as "eldest").