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How many subsets \(A\) of \(\{1,2,3,.....,100\}\) have the property that no three elements of \(A\) sum to \(101?\)

Note by Ayush G Rai 2 years ago

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*italics*

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**bold**

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1. numbered2. list

paragraph 1paragraph 2

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paragraph 2

[example link](https://brilliant.org)

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This is a quote

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2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

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There are 2^10 such subsets. Since 1+2+... + 10 = 55, there is no subset that sums to 101.

Instead of posting each of these problems as individual notes, my suggestion would be for you to post them together in a single note.

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i have edited the question.try it and also the other two parts of combinatrics.

good one! i will surely make it in a single note.

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestThere are 2^10 such subsets. Since 1+2+... + 10 = 55, there is no subset that sums to 101.

Instead of posting each of these problems as individual notes, my suggestion would be for you to post them together in a single note.

Log in to reply

i have edited the question.try it and also the other two parts of combinatrics.

Log in to reply

good one! i will surely make it in a single note.

Log in to reply