Turning heads
You are sitting at a table. On the table are 887 coins. 113 of the coins are heads up, the rest are tails up. You have to create two sets of coins. Each set must end up with the same number of heads facing up. That sounds easy. Unfortunately, it is totally dark and you can't feel which side of a coin is which. How can you do it?
Labels: logic
posted by Chris at
5:42 PM
27 Comments:
No torches or other lighting etc.
Get a cup of coffee.... wait til the sun comes up
Two sets... Easch set has one coin
stand each coin on it's edge!
flip them and hope for the best
Anonymous, 8:29 PM - OK, but how do you make sure that both coins are the same way up?
Ok, I know that you cant figure out which is which this way, but it might help someone else out.
Flip them all over and split them into two piles. That way, you will have 774 heads up coins. After that, I'm lost.
Hey.... i"ve come very close to the answer.... works 50% of the time
.... but am stuck on the last point.... i have divided it into 2 equal piles... nd have one coin left in the center.... if the coin in centre is tails then the 2 piles have equal number of heads nd i have the answer... but if coin in centre has heads then one of the piles has one heads less.... im stuck there as in how to figure out which pile to add the coin to....
will post answer after 20 mins....
Hi Chris, choose 113 and 774 coins,
flip all 113. The number of heads in both parts will be equal then.
Ok.... First flip all the coins then u will hav 774 heads nd 113 tails... now divide the coins into batches of 339... u will have 3 such batches nd u will have 96 coins left.... now put 1 batches in each of the piles nd add the third batch to the left over 96 coins... so you have 2 piles of 339 coins nd 435 coins in the centre... now divide those 435 coind in 2 equal batches of 217 coins nd add 1 batch to each of the piles nd u will have one coin left in the centre.... now if the coin in the centre is tails then both the piles have equal number of heads(i did a number of tries manually but with a smaller number of coins)... But if the coins in the centre is heads then one of the piles has one heads less... So im not able to figure out the last step.... but it still works 50% of the time....
Sorry a little mistake in the above post.... i meant to say that make 2 batches of 339 coins nd there will be 209 coins left in the centre of the table.... nd then again 2 batches of 104 coins to each of the piles nd one coin left in centre.... sry for the miscalculation....
Sry... wrong answer.... but i tried it 30 times nd it workes every times.... i dnt knw y... my hands must be lucky i guess.... but its logically wrong...
quantense got it.
Vishav_011, have you considered a career in alchemy? ;) I've no idea how close you got on your last try, it made my head hurt following your argument. Thanks for having a go, and the same for everyone else.
Vishav, out posts crossed. I ws referring to your last magnum opus.
PS The numbers I chose were an attempt to throw everyone off the scent. I could just as well have said 1 coin was heads and 1 was tails (2 coins altogether).
Chris... There are no lights so we are not able to see which of the coins are heads or tails in the first place so how can we choose 113 coins (i assume u meant the 113 coins that are heads up.... ) nd flip them ....
Vishav, it means random 113 coins. I should provide a solution. Among that 113 there are a heads and 113-a tails, among the rest 774 there are 113-a heads and 661+a tails. When you flip all coins among 113 group you will result in inverse distribution among them: 113-a heads and a tails. Now the number of heads and tails is the same.
Thanks quantense. Nice explanation. Also thanks for not giving the full explanation straight away.
I'm so relieved that the answer wasn't given on the first post :) I can't tell which problems are going to last more than a few minutes.
Just flip a single coin!
You start out with 113 heads and 774 tails.
If you flip a heads to a tails, you have 112 heads (2 sets of 56).
If you flip a tails to a heads, you have 114 heads (2 sets of 57).
ah.. disregard my post above.. I just read quantese post.. well done..
EB, consider your post disregarded :)
when the answer will be given
Hi gattu. quantense has given the answer and the explanation.
Isn't it possible to just flip one coin, which would make for an even number of heads (and a even number of tails) then just make two piles?
no
turn the light on
weep
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