Question Number 189625 by Rupesh123 last updated on 19/Mar/23
Commented by Rupesh123 last updated on 19/Mar/23
Can you explain?
Answered by Frix last updated on 19/Mar/23
$$...,{n}−\mathrm{1},{n},{n},{n},{n},{n},{n},{n},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{1},{n}+\mathrm{2},... \\ $$$${n}×{k}+\left({n}+\mathrm{1}\right)\left(\mathrm{7}−{k}\right)=\mathrm{365} \\ $$$${n}=\frac{{k}+\mathrm{358}}{\mathrm{7}};\:{n},{k}\in\mathbb{N};\:\mathrm{0}\leqslant{k}\leqslant\mathrm{7} \\ $$$$\mathrm{only}\:\mathrm{possibility}\:\mathrm{is}\:{k}=\mathrm{6}\:\Rightarrow\:{n}=\mathrm{52} \\ $$$$\mathrm{52}+\mathrm{52}+\mathrm{52}+\mathrm{52}+\mathrm{52}+\mathrm{52}+\mathrm{53}=\mathrm{365} \\ $$
Commented by Rupesh123 last updated on 19/Mar/23
Excellent!
Answered by talminator2856792 last updated on 22/Mar/23
$$\:\:\frac{\mathrm{365}}{\mathrm{7}}\:=\:\mathrm{52}\:+\:\frac{\mathrm{1}}{\mathrm{7}}\:\: \\ $$$$\:\:\Rightarrow\:\mathrm{the}\:\mathrm{row}\:\mathrm{is}\:\mathrm{six}\:\mathrm{52}'\mathrm{s}\:\mathrm{and}\:\mathrm{one}\:\mathrm{53}\:\: \\ $$$$\:\:\mathrm{middle}\:\mathrm{number}\:\mathrm{is}\:\mathrm{52}\:\: \\ $$