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Number of non-negative solutions of an equation like x + 2y + 3z = n

This type of question, asked 2 times: 1 Feb 2024, 4 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    1 Feb 2024

    82
    The number of elements in the set S={(x,y,z):x,y,z∈Z,x+2y+3z=42,x,y,z\mathbf{S = \{(x,y,z):x,y,z \in Z,x + 2y + 3z = 42,x,y,z} ≥0}\geq 0\} equals

  2. Question 2

    4 Apr 2026 S2

    67
    Let A={(a,b,c):a,b,c\mathbf{A = \{(a,b,c):a,b,c} are non-negative integers and a+b+2c=22}a + b + 2c = 22\}. The n(A)n(A) is equal to :

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