How many distinct chess games are possible, and which is the longest?

wait, you cannot multiply by 50 (49 is correct) for each half move!

118*100 is wrong.  you cannot multiply by 100 (max 98*2=98)

furthermore, maximum possible pawn moves is certainly below 96.

@233 

equal slices means their shape is identical.

moreover that doesnt give equal volumes. outers are larger in volume.

...

I think we answered that question of how many moves back on page 3 or so. Multiplying by 100 is correct, because it is 1 capture/pawn + 99 filler = 100 halfmoves. So (96+22)*100 is right. Then subtract 3 from the answer because reasons. (Issues with side-to-move in the proof game.)

For the pizza... eh. 11 is a weird number. Hubcaps? Coins? A defective clockface? I know for 37/38 there's a roulette wheel, so if you ever have 36 friends over...

Watch the wording of the question. Time is for a reason there. If you have time, can you cut it into 11 pieces?

Put it on a turntable of known frequency and make cuts at the same location at calculably appropriate timings? Put it on a clockface and cut when some hand passes some calculable marking? Or perhaps sillier, a pizza sundial?

Think about how many times the small and big arm of a clock points in the same direction and at what angles. There is a small math there about angular frequencies and modulo division and there you are.

Put the pizza on a clock. Start at midnight. Cut at the location of the hour hand every 1 hour 5 minutes and 27 seconds.

how long will it take?

Ah, that old chestnut. Did that calculation going through some old puzzle book somewhere, can't be bothered to do it again.

Now that you mention it, the trick also works if you don't have a lot of time. Just manually turn the clock to each required "time" and you can do all 11 cuts before the pizza gets cold.

Just under 11 hours. Yeah it's better not to wait!

I'd rather have a perfectly cut cold pizza than a hot pizza with irregular slices!

Hot pizza irregular for me pls!!!

I could not be more explicit than 'if you have time' in the question. I could not say 'if you a have a clock', for it would have given away the solution.

This was Predrag Minic's ingenious and very heavily upvoted answer to Quora question:

https://www.quora.com/Out-of-the-Box-Thinking/What-is-the-easiest-way-to-cut-a-pizza-into-11-equal-slices

 ( received 4600+ votes, 123+ comments and 49 shares )

There is also an interesting geometric solution under the same link ( Lewis Chen's answer ):

ahh, yeah clever. in evenly spaced intervals, the clocks minute and second hands will align 11 times in a 12 hour period. If you mark these positions you can do 11 cuts without much dificulty(even though your pizza will be quite cold). I wonder though, can this be done with straight-edge and compass geometry? transcendental numbers are very hard to deal with in straight-edge and compass geometry(can you square the circle?).

what is the maximum number of pawn moves?

Lewis Chen's answer is way better because it uses a compass which is completely exact.  The watch thing is well known but cheesy..

Yes, Lewis Chen's construction that I just posted is straight-edge and compass. Just the slices don't have identical shape only identical area.

The Kagan Puzzle drives me nuts. I have figured out that none of the captures with the queen (rook, three pawns) seem to work, neither does the Bishop takes queen move.

Pawn to g5 frees the file for the rook, but I don't see anything clear.

This puzzle is really hard. So now I am looking at every (!) legal move. Unfortunatly very few can be ruled out from the get go.

Never give up with chess puzzles.