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Friday Puzzler -- four ages

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Friday Puzzler -- four ages

#1

Friday Puzzler -- four ages

Alex Y

This is a puzzle about four people's ages, all integers less than 50.

Each of Ann, Bill, Carol, and Dennis wrote down their ages on post it

notes for all to see. They were each given a calculation to perform.

Ann, who was the youngest, just had to add the four ages, and got 60.

Bill was to add up products of all possible pairs, and got 1319.

Carol was the oldest and was asked to find the sum of the reciprocals

and got 0.2844 (approx)

Dennis was second youngest and had to find the product, and arrived at

62832.

When I checked their answers, I found that all were correct

except Dennis's result, which was too high. In fact he had made a small

error less than 6 in one of the ages on the post-it notes.

What were the ages of Ann, Bill, Carol, and Dennis?

Re: Friday Puzzler -- four ages

#2

Re: Friday Puzzler -- four ages - a start

Larry Barrett

Dividing the sum of their ages (60) by 4 = 15, which must be the average of their ages. Dividing the sum of the reciprocals (.2844) by 4 and taking the inverse of that = 14. Also note that for a given number, lowering that number increases its reciprocal.

A spreadsheet and trial and error seems necessary to go much further.

If their ages are 10, 13, 18, and 19 the resulting sum, sum of reciprocals, sum of product of pairs, and product is 60, .2851, 1323, and 62244 if the 10 is replaced by 14. Close, but no coconut (borrowing Derek's phrase).

Re: Friday Puzzler -- four ages

#3

Trial and Error

Henry Higginbotham

No spreadsheet--just an old HP11c.

Larry's suggestion that reciprocals might be the easiest way to zero in on the answer seemed right. I started with a wildly wrong set (40, 8, 7, 5) and changed the mix until, on the 21st try, I got the reciprocals to agree with 0.2844, and the other answers agreed also, with Dennis mistaking a 2 for a 7.

Ann is 11.

I wish I could say I used a fancier method than brute force, but hey! it works for hackers sometimes.

Re: Friday Puzzler -- four ages

#4

Re: Trial and Error

Larry Barrett

... and only one of them is old enough to buy a beer.

Re: Friday Puzzler -- four ages

#5

Nice job, Henry

Alex Y

And interesting to note that Dennis made the mistake on his OWN age.

Interesting that no-one went with the factorization of the product of ages. I did, but it didn't take me far.

👍 This page answered my questions

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