Given four numbers x, y, z, n. The task is to find the number of solutions for the equation x + y + z <= n, such that 0 <= x <= X, 0 <= y <= Y, 0 <= z <= Z.
Input: x = 1, y = 1, z = 1, n = 1 Output: 4 Input: x = 1, y = 2, z = 3, n = 4 Output: 20
Approach: Let’s iterate explicitly over all possible values of x and y (using nested loop). For one such fixed values of x and y, the problem reduces to how many values of z are there such that z <= n – x – y and 0 <= z <= Z.
Below is the required implementation to find the number of solutions:
- Number of integral solutions of the equation x1 + x2 +.... + xN = k
- Find the number of solutions to the given equation
- Number of non-negative integral solutions of sum equation
- Number of integral solutions for equation x = b*(sumofdigits(x)^a)+c
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- Find the missing value from the given equation a + b = c
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