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Question Number 202598 by cortano12 last updated on 30/Dec/23
Answered by MM42 last updated on 30/Dec/23
$$\mathrm{780}\: \\ $$$$ \\ $$
Commented by MM42 last updated on 30/Dec/23
Commented by MM42 last updated on 30/Dec/23
$$\frac{\mathrm{40}×\mathrm{40}−\mathrm{40}}{\mathrm{2}}\:=\:\mathrm{780}\: \\ $$
Answered by mr W last updated on 30/Dec/23
$${x},{y}\geqslant\mathrm{1} \\ $$$${x}+{y}<\mathrm{41} \\ $$$${x}=\mathrm{1},\:{y}=\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:...,\:\mathrm{39} \\ $$$${x}=\mathrm{2},\:{y}=\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:...,\:\mathrm{38} \\ $$$$... \\ $$$${x}=\mathrm{39},\:{y}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{39}=\frac{\mathrm{39}×\mathrm{40}}{\mathrm{2}}=\mathrm{780}\:{points} \\ $$