Pancake Numbers - Numberphile

Katie Steckles on Pancake Numbers..
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[fluffykitten]

My pancake number is n+1. It means one more please.

[RandomFacades]

Wouldn't the upper limit on a stack of twenty be nineteen's value + 2?
Because you can use a flip to get the largest to the top, then a flip to get the largest to the bottom. At that point, you can just treat the above ones like a stack of nineteen.

[NGC-]

The most efficient way to flip 20 pancakes is to flip them directly into your mouth

[magicalmond]

It also worries me that they have just random 'fake' pancakes just on hand. Like what else would they have them for??

[trinmyster]

I’m on the bus, but nothing can pass the numperphile vids

[raimundozubelzu]

Best math video to watch while breakfast

[klaasdeboer]

This math video inspired me into microbiology and chemistry, making pancakes with yeast!

[albertb]

I first read "Parker Numbers"

[RussianShadowStorm]

4:30

"Paint me like one of your French girls."

[dangrogan]

Correct me if I'm wrong (and I very well could be wrong), but if P19=22 then shouldn't the bound for P20 be 24? Think about it recursively. Suppose you have any stack of 20 pancakes sorted any way. You flip the stack wherever the largest pancake is so that the largest pancake ends up on top. Then you flip the whole stack so the largest one is on bottom now. Now, above the largest pancake is a stack of 19 unsorted pancakes. Thus it takes 22 moves at most to sort those 19 pancakes. This uses a mac of 24 moves. Essentially, the bound for Pn should be P(n-1)+2

[miallo]

The pancake number any number can only be bigger by 2 than the one for n-1 since you could do the trick of flipping the biggest to the top and then to the bottom and then start with the optimised way for n-1. So what I am saying is that the upper bound for 20 pancakes mentioned at 4:13 shouldn't be 35 but 24.

[roeesi-personal]

Actually, we can easily know that the pancake number of 20 is much less that 35 or 32, but actually 24 or less.
To order 20 pancakes in 24 moves we can just bring the largest pancake to the bottom in 2 moves, as you have shown, and then order the 19 remaining pancakes in 22 moves – 24 moves in total.

[SamuelJSAdamsI]

Surely the upper bound for 20 is 24. My algorithm: 1. Put largest pancakes on top of stack
2. Flip stack
3. Follow algorithm for 19.
Upper bound for 19 is 22

[andrewkovnat]

Ahh, sorting algorithms. Why are they so big on YouTube all of a sudden?
Oh right, YouTube recommendations are a bit bugged.
I saw ONE sorting algorithm video in like 2014, and they have always been showing up.

[ben.woodworth]

For 20 pancakes, can't we say that the upper bound is 24 instead of 35? You can get the largest pancake to the bottom in 2 flips, and then solve the remaining 19 pancakes in 22 (the upper bound for 19 pancakes).

More generally, can't it be said that the next pancake number can't be more than 2 greater than the previous?

[marcelweber]

Not sure whether I'm more stunned about the crazy ideas mathematicians have and spend their lives with or these crazy things actually help one day by solving "real" problems.

[trangium]

If you had 20 pancakes, they'd all fall over.

[schmegnu]

If you knew the pancake number for 19, you would - in case you got 20 pancakes - just flip the largest one to the bottom (would take two flips at max). Then you never touch the biggest pancake again and your upper bound should be 2 + the pancake number of 19.

[katlin]

I never thought that the word "pancake" and "number" would go together

[theblazingbarbarian]

Awesome Nail and Gear poster in the background. Framed too!