How odd!
Is the the number 124 (in base 5) odd or even? More generally, how can you tell if a number in any base, is odd or even? (Don't worry about the obvious issues for bases > 10).
Labels: mathschallenge
posted by Chris at
7:45 PM
5 Comments:
124 is 444 in base 5.
But changing the base should not change an even to odd.
5 in base 5 is 10, but it is still and odd number... A rose is a rose....
Am I missing something?
124(base 5) = 1*25 + 2*5 + 4 = 39(base 10). So it's odd.
A number in an odd base is odd if there are an odd number of odd digits. (That's 4 odds in one sentence!).
A number in an even base is odd only if the last digit is odd.
Alternatively, for an odd base, if the sum of the digits in the number is odd then the number is odd.
Yes, I do think Ragknot is missng something . . .
Oh, I read the post differently. I read it without the the parentheses.
Is the number 124 odd or even in base 5?
Soz about that, I didn't notice the ambiguity.
Wiz got the full answer.
In base b a number N is written:
N = d[n] * b^n + d[n-1] * n^(n-1) + ... + d[1] * b + d[0]
Where d[n] represent the n the "digit" of the number (starting at 0).
In mod 2 =>, if b is even, then
N = d[n] * 0^n + d[n-1] * 0^(n-1) + ... + d[1] * 0 + d[0] = d[0].
So the number is even if the last digit is even.
If b is odd, then b and all powers of b, are divisible by 2 with a remainder of 1 =>
N = d[n] * 1^n + d[n-1] * 1^(n-1) + ... + d[1] * 1 + d[0]
N = d[n] + d[n-1] + ... + d[1] + d[0].
So add the digits. If the sum is odd, then so is the number.
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