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.
2 answers
I'm sorry, N=a+b^2
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
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
1 answer