dark coin riddle

Logic Level 1

You have a 100 coins, that are silver on one side and gold on the other; both sides feel and taste the same so you can not distinguish between the silver face and the gold face by the sense of touch or taste. Is it possible to split the pile of coins in to two parts, where each halve has the same amount of gold face up as the other pile, if the only sense you can use is touch, and all you know is that there are 20 gold faces faced up and, hence 80 silver coin faces faced down?

Assumptions :

if one pile has 7 gold faces faced up, the other pile must have 7 gold faces up as well
you can not hear, smell, see or taste anything, but only can touch

yes no

4 solutions

Mikael Bashir
Jun 1, 2018

Take any 20 coins from the pile of 100 coins, and flip the pile over to get two equal piles - it really is that easy! For example, if you take 20 coins and 7 of them are gold facing up ways, then there will be 14 silver facing up ways coins, and also the other 14 gold facing up ways coins will be in the pile of 80 coins; if you flip the pile containing 20 coins, the 14 silver facing up ways coins will become 14 gold facing up ways coins, hence 2 piles containing an equal amount of gold facing up ways coins. This will work for any scenario, whether all the coins are in the pile of 20 coins, or none of them are in there.

How do we get two equal halves using this method? As I understood it, we had to split the coins into two equal parts, and then make sure each half had the same number of gold coins facing up.

Akash Gaonkar - 2 years, 12 months ago

The question asks to split the pile of 100 coins into two parts/piles. And to clear any confusion, when I say two equal piles, I mean to say two piles that have the same amount of gold faces facing up, and do not mean two piles with the same number of coins.

You can only use this method if you know how many gold faces are facing up ways in the pile of 100 coins, and in this problem, we have 20 gold faces facing up.

Your first step will be to take $any$ 20 coins from the pile of 100 coins, so that you have a pile of 20 coins, and 80 coins.

Your second step will be to flip all the coins in the pile of 20 coins. This will give you 2 piles that consist of the same amount of gold faces facing up.

I will prove that this works for any scenario, using algebra. Say $x$ is the amount of coins in the pile of 80 coins, than there will be 20 - $x$ coins in the pile consisting of 20 coins. If we substitute $x$ for 13, we get 13 gold faces facing up ways coins in the pile of 80 coins, and 20 - 13 = 7 gold faces facing up ways coins in the pile of 20 coins. 13 + 7 = 20 , and when you flip the pile consisting of 20 coins, the 7 gold faces facing up will become silver faces facing up, and the 13 silver faces facing up will become 13 gold faces facing up ways coins. 13 = 13 , hence two piles consisting of the same amount of gold faces facing up.

Mikael Bashir - 2 years, 12 months ago

I have to say, the "Is it possible to split the pile of coins in to two equal parts(...)" has completely misled me into thinking the piles had to have the same amount of coins..

Filipe Lopes - 2 years, 11 months ago

On your explanation, you said that if there were 7 gold facing up coins, then there would be 14 gold facing up coins. Wouldn't that be 21 coins??

Adrian Ma - 2 years, 4 months ago

If you read my explanation again, you will find that I said, 'If you take 20 coins and 7 of them are gold facing up ways, then there will be 14 silver facing up ways coins.' Sorry for any misunderstanding.

Mikael Bashir - 2 years, 4 months ago

Nick Turtle
Jun 7, 2018

Divide the 100 coins into two piles of 20 coins and 80 coins each. If the first pile has $x$ gold, it has $20-x$ silver. The second pile will have $20-x$ gold and $60+x$ silver.

Now, if you flip all of the coins in one pile, you swap the number of gold and silver in the pile. So, if you flip the first pile, it will have $20-x$ gold and $x$ silver. The number of gold in both piles is now the same.

Francis Naldo
Jun 10, 2018

Get 20 coins and flip them. This will be your second pile.

Let X be the coins you flipped are originally gold (face). The number of coins on the first pile facing gold side will be reduced by X. $20 - X$ . Among the 20 coins you placed in the second pile, there will be $20 - X$ coins originally facing silver side. After flipping the coins, those silver side will become gold side.

Stephen Mellor
Jun 7, 2018

If you want the full problem and answer in video form, go to this link

it's on ted ed

Bách Hữu Trần - 1 year, 2 months ago

dark coin riddle

4 solutions

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