# Needle in a haystack

Cambridge dictionary defines the phrase “find a needle in the haystack” as “something that is impossible or extremely difficult to find, especially because the area that you have to search is too large”. If we are being really serious, how difficult it is to find a needle in a haystack, be specific.

## Needle

There are many needles for sale on Amazon, here is one of the most popular ones, there are in total 23 needles in the pack with 0.317oz of weight. If we first convert weight to metrics, 0.317ounce = 8.98grams. That means each needle weight on average 0.4g/piece. Depending on how much the package itself weigh, the real weight should even be less than 0.4g.

When it comes to needle size, just like different clothes manufacturers have different size chart, different needle manufacturers have their own manual explaining their size system. For example, John and James is a popular UK brand and they have a size chart here. The smallest needle that I can find is their JJ195 for tapestry and cross stitch with size28 of length 32.5mm and diameter of 0.53mm. The volume for a cylinder of that shape is pi * (d/2)^2 * l = 7.17mm^3.

Plain steel’s density about 7.85 g/cm3 (reference). The inferred weight is about 0.06g. This is a significantly smaller number compared to the 0.4g previously guessed. However, if we take another look, the previously estimated 0.4g was based on relatively medium size needles. Even in JJ’s manual, you can find many needles with a larger diameter size, ranging from 0.53 to 2.34, if we moderately increase the needle size by only a factor of 2, that will increase the volume by a factor of 8. 0.06g * 8 ~ 0.48g which doesn’t sound that crazy at all.

To summarize, a small needle can weight 0.06g with a size of 7mm^3.

## Haystack

For lack of better term, haystack is merely a stack of grass. They exist in many forms. On modern farms, hays are usually handled by industrial machines and packed into square or round shape of various sizes.

John Deere is one of the larges manufacturers for this kind of industrial machines. The type of machine that pack loose hays into compact hay bales is called baler. For example, 450M round baler.

Interestingly, you can find the baler specifications in the user manual. The largest bale is probably packed by 560M with the weight of 1089kg. And volume of 4.13 m^3.

## Methods

### By Weight

needle ~ 0.06g, haystack ~ 1089kg.

haystack / needle = 1089kg/0.06g=18,150,000.0 = 18M

### By Volume

needle ~ 7.17mm^3, haystack ~ 4.13m^3

haystack / needle = (4.13*1000)^3/7.17 = 9,824,964,714 = 10B

## Conclusion

Fun fact, there are about 7.8B people in the world, and finding a needle in a haystack is about the same odds of finding another person on earth. Long story short, it is hard to find a needle in a haystack. Hold on to your needle and don’t drop it.