144
In what number bases does 144 represent a square number.
Labels: mathemagic
posted by Chris at
8:06 PM
Friday, February 19, 2010
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11 Comments:
Wiz and Cam. I've resolved the Six take a test... 35% interpretation.
18 squared is 324
which is 144 in base 16
In any base n, 144 = n^2 + 4^n + 4 = (n+2)^2.
So, it would be a square in any base (>4 obviously).
I'll look at Six Take A Test.
7 squared is 49 which 144 in base 5
Let's see if we can derive that.
The numeral string 144 in base b represents
b^2 + 4*b + 4
which is
(b+2)^2
Therefore it is ALWAYS a perfect square, no matter what base (as long as the base is greater than 4)
144 base 5 = 49
144 base 6 = 64
144 base 7 = 81
144 base 15 = 256
144 base 16 = 324
144 base 238 = 57600
Wiz beat me :-)
I always refresh the question page just before I publish my answer as it often takes several minutes to type the answer after I've downloaded the question.
That way I don't publish if I then find that someone has just got in ahead of me with the same answer.
Wiz, why not publish anyway. It's nice to have a confirmation.
Needless to say, you and Ross did it.
Chris, I've responded to your latest post in Six Take a Test.
This may not be what you expect, or want.
Up till now we had two answers of to the puzzle of 35% (Cam & me) and 95% (you). The latter is the official correct result.
I've entered another horse in the race, which I rather fancy, namely 47.62%.
I think I'd put my money on this one.
Go to the post to see why.
12
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