ap

Let the number of 4's be x and 6's be y.

then 4x + 6y = 100

x, y are positive integers.

Hence, 6y = - 4x + 100.

y = -2x/3 + 50/3 = -2(x+25)/3

The solution can be obtained graphically or tabulating y for selected value of x.

For example,

y = 0, then x = 25, here the player will have to hit 25 4's.

Similarly find set of integers satisfying the equations, and we'll have the number of ways required equal to the set of those integers.

Regards,

Team,

TopperLearning.