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Are You Good With Task? - 6/2/2010 10:32:53 PM

GoddessDumore

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A group of teenagers decided to multiply their ages together. This is the number they computed: 2,995,049,820,672,000

Find the exact ages of the teenagers and how many were in the group.

There is a real number.

To help teens ages run from 13 thur 19

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RE: Are You Good With Task? - 6/2/2010 10:42:12 PM

wittynamehere

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quote:

ORIGINAL: GoddessDumore
Find the exact ages of the teenagers and how many were in the group.

If one were to find the ages of all the teenagers, that would already tell you how many there were, so the second part of the question can be dropped.

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RE: Are You Good With Task? - 6/2/2010 11:25:26 PM

shallowdeep

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Prime factorization of 2995049820672000:
2^12, 3^7, 5^3, 7^2, 13^2, 17^1, 19^1

Recombining to get ages in the specified range:
2^4 = 16 (2)
2*3^2 = 18 (2)
3*5 = 15 (3)
2*7 = 14 (2)
13 (2)
17 (1)
19 (1)

So the group consists of two 13-year-olds, two 14-year-olds, three 15-year-olds, two 16-year-olds, one 17-year-old, two 18-year-olds, and one 19-year-old. Thirteen people in all.

Am I procrastinating? Yes.

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RE: Are You Good With Task? - 6/3/2010 1:42:23 AM

VaguelyCurious

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Damnit, you beat me.

But that's how I would have done it, had I seen it first.

We covered prime factor decomposition in school when I was twelve. This is the same stuff we did then, but with bigger numbers-not exactly complicated...

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RE: Are You Good With Task? - 6/3/2010 2:45:14 AM

shallowdeep

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Hmm. The UK seems to be lagging with maths then; I'm pretty sure we covered it in 4th grade (typically ages 9-10). Maybe if you didn't have to spend all that time writing an additional 's' on your papers...

More seriously, there was a priori knowledge that the factors had an upper bound of 19 in this problem, so factorization was easy; but, as a rule, mere "bigger numbers" usually do start adding a huge amount of complexity to prime factorization problems. General and fast prime factorization algorithms are still very much an area of research – and it's not an easy problem. The complexity of factoring really big numbers actually underlies many public-key cryptography systems, like RSA... stuff that lets you use the Internet securely. So the field is more interesting than it might seem. But, yes, this problem was trivial.

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