The Clever Way to Count Tanks - Numberphile

See brilliant.org/numberphile for Brilliant and 20% off their premium service & 30-day trial (episode sponsor)

You didn't just pull out the first and last, but also the middle tanks 15&16!

Pointing out that lower numbers are more likely is such a good observation. Brady keeps highlighting his genius video after video.

6:33 I love the way the turrets are pointing at their actual positions in the number line :)

Watching James Grime explain mathematics is such a joy.

In arms production it's fairly common for factories to assign serial number ranges to particular products in advance, so the serial number ranges having gaps within them is relatively normal. It's also normal for them to start production at something like 10,000 if they expect to make in the tens of thousands of that particular item, that way they all the items are serialized, but they also maintain the same number of digits in their serial number for uniformity without using a bunch of leading zeros. Overrunning that serial range usually results in a letter prefix or suffix being added.

A company I worked for made computers & peripherals and used 64 bit random serial numbers. They had multiple manufacturing sites, and calculated that the odds of selecting two identical numbers was smaller than human bookkeeping and errors trying to coordinate multiple product lines.

I love how british "they have a bit of a spy" is

His reaction to tank 30 immediately raised suspicion and I would have said "yeah, that's 30 tanks in the bag."

Tanks for sharing

James: There are 30 German tanks in the bag. Chuikov: We were aware of that.

Spies be like "tank you very much" but the mathematicians be like "tanks but no tanks"

Excellent. I did laugh at the #1 and #30 thing. Always like Dr Grimes in these videos, I could listen to him just tel me interesting stuff all day.

it would also make sense to calculate the average of the samples and multiply it by 2 as the average of consecutive numbers starting at 1 would be about n/2 and the average of the samples would also approach the same value.

At 6:36 you were right on! The gap below your minimum observation WAS equal to the gap above the maximum observation and the true number of tanks!

I love the "German Tank Problem." There's a great video on YouTube showing this method of counting the Commodore 1571 Disk Drives. Using this technique for "other real-world problems" is a fun exercise.

My immediate thought was that the average of a random subset should be the same as the average of the whole, so the number of tanks should be twice the mean of the picked ones 2*(1+15+16+23+30)/5=34 for the first pick and 2*(3+10+15+18+24)/5=28 for the second. My guess is that they used multiple estimate methods and weighted the results depending on inherent uncertainties/errors of the methods

The disgust in Dr. Grime's voice at 2:24 when he says "I'm NOT going to let you feel the weight of the bag! [Are you daft?]"

Tanks for sharing!!!

I know it's irrelevant, but there's the old joke about letting three sheep loose in a field, but first labelling them "1" "2" and "4" so the person rounding them up spends ages looking for the 3rd.