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outrun
Topic Author
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### coins in a dark room

Pantalopus is in a dark cave with a pile of 100 coins. Pakanina (Pantalopus Grandpa) told you that 20 of the coins are heads side up and the rest are tails side up. It's your job to make Pantalopus make two piles of coins that have the same number of heads side up coins. The room is in total darkness and Pantalopus tells you via the device depicted below that each coin feels the same on both sides.

What to do?

No googling of course.

Paul
Posts: 10771
Joined: July 20th, 2001, 3:28 pm

### Re: coins in a dark room

Set 20 to one side and turn them over.

outrun
Topic Author
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: coins in a dark room

Set 20 to one side and turn them over.
That's brilliant! (and quick)

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### Re: coins in a dark room

Solution 2: cut every coin in half, separate the two sets of half-coins, pair each set of 100 half coins to make 50 coins.

Paul
Posts: 10771
Joined: July 20th, 2001, 3:28 pm

### Re: coins in a dark room

Set 20 to one side and turn them over.
That's brilliant! (and quick)
I’ve heard this before. I was in the back of a taxi with Bruno Dupire and another quant or two. One of the others asked this question. I was just as quick with the answer then!

There’s not much you can do with piles of coins! You can separate them into more piles (you’ve got to do that anyway at some stage and there’s no point in more than two piles) and you can turn them over. So it’s just a question of how many you move. It’s going to be either 10 or 20. Easy!

outrun
Topic Author
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

### Re: coins in a dark room

Set 20 to one side and turn them over.
That's brilliant! (and quick)
I’ve heard this before. I was in the back of a taxi with Bruno Dupire and another quant or two. One of the others asked this question. I was just as quick with the answer then!

There’s not much you can do with piles of coins! You can separate them into more piles (you’ve got to do that anyway at some stage and there’s no point in more than two piles) and you can turn them over. So it’s just a question of how many you move. It’s going to be either 10 or 20. Easy!
Nice story. Were there any more puzzles during that trip?

And couldn't one of the quants stop talking about the taxi number being 1729?.. because then I probably know who it was.

Collector
Posts: 4607
Joined: August 21st, 2001, 12:37 pm

### Re: coins in a dark room

I would simply have called Bruno and asked if he remembered the solution that Paul gave him in the taxi. And if the cell phone signal not could penetrate the cave I would just have turned on the light on my phone! Why make it so complicated? (Traders versus Quants I guess)
the taxi number being 1729?.
"I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Cubing the Cube? Unfortunately then we need to call someone else than Bruno. Or did he tell about it on another cab ride?

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