There are 100 points on a circle

[Night_Flower]

There are 100 points on a circle.The first one - "1", the point which is two points after the first - "2"and so on, while there are 98 points. Which is the smallest number, which is written on the points, where "98" is?

[dancho]

I think it is 99
But I am not shure

[dancho]

It is 99

[Ellery Cade]

Factoring all the numbers into primes:

t e^2 n = 2^2 * 13
t^2 i l = 7 * 11
t a l^2 = 3 * 11^2

From the second of these equations, it is clear that t = 1, otherwise there would be a prime number with exponent >= 2 in the right-hand-side. Assuming different letters stand for different numbers, we now also know that l = 11 (from second and third equation). This gives us a = 3, i = 7. If all numbers are different, e can only be 2.
So tattle becomes t^3 a l e = 1^3 * 3 * 11 * 2 = 66.

[Math Tutor]

Interesting solution Ellery Cade.
Thank you for joining us.

[deOmair]

that was interesting...




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