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How to calculate how many skips I need to make to get a percentage.

i.e. Let's say I have 13 million apples and I am going through each one counting and every 10 apple I place it in a different bucket, at the end I end up with a bucket with 10% of the original number of apples.

How many apples do I need to skip to get 20% in the bucket?

How many do I need to skip to get n% in the bucket?

thanks.

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yes sorry I made the change, still how do I get how many for 20%? –  luis May 6 '12 at 7:42

1 Answer 1

Convert the percentage to a fraction. For instance, $20\%=\frac{20}{100}=\frac15$. To get $20$% of the apples into the bucket, you need to put one-fifth of them into the bucket, so every fifth apple should go into the bucket. In general, if the percentage corresponds to the fraction $\frac1m$ for some integer $m$, you want to put every $m$-th apple into the bucket.

It gets messier when the percentage doesn't correspond to a fraction of the form $\frac1m$. Suppose, for instance, that you want to end up with $30$% of the apples in the bucket. $30$% is $\frac3{10}$, so you need to put $3$ out of every $10$ apples into the bucket. You can simply do it: $3$ apples into the bucket, then $7$ out of it, then $3$ into it, then $7$ out of it, and so on. There's no way to get it exactly right putting one apple into the bucket, skipping a fixed number, putting one apple into the bucket, skipping the same fixed number, and so on. The closest you can come is a sequence like this, where the red apples go into the bucket:

$$\color{red}{\text{O}}\text{O}\text{O}\color{red}{\text{O}}\text{O}\text{O}\color{red}{\text{O}}\text{O}\text{O}\text{O}|\color{red}{\text{O}}\text{O}\text{O}\color{red}{\text{O}}\text{O}\text{O}\color{red}{\text{O}}\text{O}\text{O}\text{O}|\color{red}{\text{O}}\text{O}\text{O}\color{red}{\text{O}}\text{O}\text{O}\color{red}{\text{O}}\text{O}\text{O}\text{O}|\color{red}{\text{O}}\cdots$$

That does put $3$ out of every $10$ into the bucket, or $30$%, and it almost does it with a regular spacing, but not quite.

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