Forgot to put in a maths problem - how about this:
I'm thinking of a number less than 4000. It is divisible by all the whole numbers from 2 to 12 inclusive, except for two of them, which are consecutive. What is the number?
I'm thinking of a number less than 4000. It is divisible by all the whole numbers from 2 to 12 inclusive, except for two of them, which are consecutive. What is the number?
posted by Fearnley | 2:18 PM
2 Comments:
We think we've got there in the end...
The answer must be divisible by 2, since if it wasn't, it would also not be divisible by 4, which would mean 2 non-consecutive non-divisors(!) Similarly with 3,4,5 and 6. The lowest common multiple of these is 60, so the answer must be a multiple of 60.
In which case, it must be divisible by 10 and 12. So it must also be divisible by 11, since a non-divisor cannot stand alone.
And the answer must not be divisible by 8; if it were, then 7 and 9 would be the only remaining non-divisors possible and these are non-consecutive. So it needs to be an odd multiple of 60 (i.e. 3x60, 5x60, etc).
Which only leaves
11x60 = 660
33x60 = 1,980
55x60 = 3,300
The first doesn't divide by 7 or 9
The second doesn't divide by 7 or 8 but does divide by 9
The third doesn't divide by 7 or 9
SO the answer is 1,980 which divides by all the numbers from 2 to 12 except 7 and 8.
Phew!
Peter
x
Very well done! - was this a joint effort?
The neatest way I found to solve it was to express each number by its prime factors, then look for which prime numbers you can take out which only eliminate one of the candidates. I'll probably post this so it's a bit clearer.
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