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I honestly dont feel any need to key in any values. There are 3 variables and the answer asks about values of (x,y) to be in integers. If it is silent about third variable 'l', then the number of combination depends on any integer or FRACTION value of l which will make it impossible to come-up with definite number of x and y into integers.

I honestly dont feel any need to key in any values. There are 3 variables and the answer asks about values of (x,y) to be in integers. If it is silent about third variable 'l', then the number of combination depends on any integer or FRACTION value of l which will make it impossible to come-up with definite number of x and y into integers.

I would guess it ans A.

CLARIFICATION

l is actually mod.....its not a variable...ie value of (x-4) has to be positive

PLUS we should not forget that x and y can be 4 (but not together): x=4 --> |x-4|+|y-4|=4 --> |y-4|=4, y=8 or 0. Integer values of (x,y)=(4,8),(4,0) 2 sets.

y=4 --> |x-4|+|y-4|=4 --> |x-4|=4, x=8 or 0. Integer values of (x,y)=(8,4),(0,4) 2 sets.

if |x-4| + |y-4|=0, then both x-4 and y-4 have to be positive. which means, there are following possibilities: if - x-4 and y-4 if - 0 then 4, hence x = 4 and y = 0 or 8 if - 1 then 3, hence x = 3 or 5 and y = 1 or 7 if - 2 then 2, hence x = 2 or 6 and y = 2 or 6 if - 3 then 1, hence x = 1 or 7 and y = 3 or 5 if - 4 then 0, hence x = 0 or 8 and y = 4.

Dont know if there can be more possibilities within positive numbers. Ans should be 16.

For my Cambridge essay I have to write down by short and long term career objectives as a part of the personal statement. Easy enough I said, done it...