Disclaimer: a colleague emailed this to me, i suck at math and have no clue what the answer is

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is. Great Granddad was born in the year A (where A is the product of 3 prime numbers), he was 20 years old in the year B (where B is the product of a prime number and a square number), he was 80 years old in the year C (where C is the product of two prime numbers) and he celebrated his 100th birthday in the year D (where D is even and the product of 4 prime numbers). When was he born?

# Granddad Prime

Page 1 of 1## 3 Replies - 662 Views - Last Post: 27 June 2017 - 10:42 PM

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**Replies To:** Granddad Prime

### #3

## Re: Granddad Prime

Posted 08 March 2017 - 03:53 PM

That shouldn't be that hard to figure out. You can look at the telegram and check the date of his 100th birthday, or just ask the old bastard when he was born. Boom, next.

### #4

## Re: Granddad Prime

Posted 27 June 2017 - 10:42 PM

So the answer isn't very interesting, but since you said you had trouble with this sort of problem, here's how my thinking went:

First of all, we're talking about a roughly contemporaneous date for D - this business of the telegram says, basically, we're in the long 20th century. (call it somewhere between WWI and today)

So you want four prime numbers, one of them being 2, which multiply together to give a date in this range. That was pretty simple. 10^3 * 2 puts us in the right ballpark, so I had a pretty small range to examine.

That gave me a likely date for D. Since D is even, B = D - 80 is even, so I knew that B was twice a square number. This made it very easy to check that sqrt((D - 80) / 2) was a square, which confirmed it for me. For giggles, I checked that C = (D - 20) was twice a prime number, which it was.

Looking at your link, I see that Julia's reasoning was similar to mine - the main difference is where we saw the crack in the problem. That's a useful observation if you find problems like this to be frustrating. Martin Gardner has a book called "Aha!" which is all about this sort of insight, might be useful of you're interested in getting better at these puzzles.

First of all, we're talking about a roughly contemporaneous date for D - this business of the telegram says, basically, we're in the long 20th century. (call it somewhere between WWI and today)

So you want four prime numbers, one of them being 2, which multiply together to give a date in this range. That was pretty simple. 10^3 * 2 puts us in the right ballpark, so I had a pretty small range to examine.

That gave me a likely date for D. Since D is even, B = D - 80 is even, so I knew that B was twice a square number. This made it very easy to check that sqrt((D - 80) / 2) was a square, which confirmed it for me. For giggles, I checked that C = (D - 20) was twice a prime number, which it was.

Looking at your link, I see that Julia's reasoning was similar to mine - the main difference is where we saw the crack in the problem. That's a useful observation if you find problems like this to be frustrating. Martin Gardner has a book called "Aha!" which is all about this sort of insight, might be useful of you're interested in getting better at these puzzles.

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