Posted by **CT** on Monday, April 5, 2010 at 8:06pm.

2 teams played each other recently. Team 1 scored N points, while team 2 scored M. 1<M and N<100.

The first digit of N is a, the second digit b. N-a+b^2.

The first digit of M is b, the second is a. By how many points does team M win the game? There is a mathematical way to do this, although I reached the answer by process of elimination.

- Math -
**CT**, Monday, April 5, 2010 at 8:15pm
I'm sorry, N=a+b^2

- Math -
**Reiny**, Monday, April 5, 2010 at 8:38pm
Let N = 10a + b

but N = a + b^2

so b^2 + a - 10a + b

b^2 - b - 9a = 0

b(b-1) = 9a

which tell me that the product of 2 consecutive numbers, which are less than 10, must be a multiple of 9

only possibilities

9x8 = 72 yes

8x7 = 56 no

7x6 = 42 no

6x5 = 30 no

5x4 = 20 no

4x3 = 12 no

3x2 = 6 no

2x1 = 2 no

so 9a = 72

a = 8

then b^ - b - 72 = 0

(b-9)(b+8) = 0

b = 9

N = a + b^2 = 8 + 81 = 89

M = 98

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