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Question Number 190818 by cortano12 last updated on 12/Apr/23

It is known that the set A={1 , 2, 3, ..., 100} The numbers of subsets of A which when added together are divisible by 4

$$\:\:\mathrm{It}\:\mathrm{is}\:\mathrm{known}\:\mathrm{that}\:\mathrm{the}\:\mathrm{set}\:\mathrm{A}=\left\{\mathrm{1}\:,\:\mathrm{2},\:\mathrm{3},\:...,\:\mathrm{100}\right\} \\ $$$$\:\mathrm{The}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{subsets}\:\mathrm{of}\:\mathrm{A}\:\mathrm{which}\:\mathrm{when}\: \\ $$$$\:\mathrm{added}\:\mathrm{together}\:\mathrm{are}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{4} \\ $$

Commented by safojontoshtemirov last updated on 12/Apr/23

[((100)/4)]=25

$$\left[\frac{\mathrm{100}}{\mathrm{4}}\right]=\mathrm{25} \\ $$

Commented by cortano12 last updated on 12/Apr/23

no

$$\mathrm{no} \\ $$

Commented by mehdee42 last updated on 12/Apr/23

2^(25) −1

$$\mathrm{2}^{\mathrm{25}} −\mathrm{1} \\ $$

Commented by cortano12 last updated on 13/Apr/23

how

$$\mathrm{how} \\ $$

Commented by safojontoshtemirov last updated on 13/Apr/23

formulas:2^([(n/k)]) −1 int[(n/k)]

$${formulas}:\mathrm{2}^{\left[\frac{{n}}{{k}}\right]} −\mathrm{1}\:\:\:\:\:{int}\left[\frac{{n}}{{k}}\right] \\ $$

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