Logic Puzzles

7. Flipping Coins

There are twenty coins sitting on the table, ten are currently heads and tens are currently tails. You are sitting at the table with a blindfold and gloves on. You are able to feel where the coins are, but are unable to see or feel if they heads or tails. You must create two sets of coins. Each set must have the same number of heads and tails as the other group. You can only move or flip the coins, you are unable to determine their current state. How do you create two even groups of coins with the same number of heads and tails in each group?

Submitted by julioprimo · Added 1 January 2007 · Updated 5 July 2026

Solution:

Create two sets of ten coins. Flip the coins in one of the sets over, and leave the coins in the other set alone. The first set of ten coins will have the same number of heads and tails as the other set of ten coins.

Flipping Coins Simulator

This randomly arranges 20 coins, exactly 10 heads and 10 tails. It then randomly chooses 10 coins for Group A. Flip Group A and compare the two groups.

Group A

Group B


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Comments (24)

Anonymous 7 April 2007

Your solution to the scale puzzle is flawed. You stated to use the scale only once, but your solution implies using it multiple times. Please reconsider your approach.

Anonymous 6 December 2009

I don't follow the solution to "Flipping Coins". Can you explain it in a bit more detail?

Anonymous 6 December 2009

I don't follow the solution to 'Flipping Coins'. Can you explain it in a bit more detail?

Anonymous 13 December 2009

I am not sure that the solution given for this problem is correct. Consider the situation where the first pile contains 5 heads and 5 tails, and the second set contains 4 heads and 6 tails. Flipping the coins in the first pile would result in a pile with 5 of each coin, which are not two piles containing the same number of heads and tails.

Anonymous 16 December 2009

I've noticed that the solution proposed to 'Flipping Coins' seems incorrect. To create two groups with the same number of heads, one must separate a group of 10 coins and flip them all.

Anonymous 24 December 2009

The question about flipping coins is incorrect. There should be 20 coins, 10 heads and 10 tails, instead of 100 coins for the solution to be correct.

Anonymous 30 December 2009

Problem #7, Flipping Coins, is wrong. Two groups of 10 coins chosen at random does not guarantee that for every tail accounted for in one group of ten, there is a head in the other group of ten.

Anonymous 30 December 2009

The method described for flipping coins does not guarantee equal heads and tails. The original problem should be reviewed for accuracy.

Anonymous 25 January 2010

Pertaining to the Flipping Coins puzzle, there are a hundred coins sitting on the table, ten are currently heads and ninety are currently tails. You must create two sets of coins, each set must have the same number of heads.

Anonymous 25 January 2010

The solution to the Flipping Coins puzzle is incorrect. You cannot create two sets with the same number of heads and tails if one set has 10 tails and the other has 9 tails.

Anonymous 27 January 2010

The solution to 'Flipping Coins' doesn't make sense to me. If you don't know which are heads or tails to begin with, then the selection for each group of 10 is random. Flipping one group wouldn't give the same number of heads and tails.

Anonymous 3 February 2010

It seems to me that the puzzle has no solution. I tried the solution offered and something seems wrong to me. It says "Create two sets of ten coins" but we don't know if they are heads or tails.

Anonymous 3 February 2010

I tried to solve 'Flipping Coins' and it seems to have no solution. If we randomly pick 1 head and 9 tails in one group and 2 heads and 8 tails in the other, flipping one group won't give the same number of heads and tails.

Anonymous 5 February 2010

The solution to the Flipping Coins puzzle is to create two sets of ten coins. Flip the coins in one of the sets over, and leave the coins in the other set as they are.

Anonymous 10 February 2010

The puzzle 'Flipping Coins' is incorrectly stated. The correct wording should be that you want to end up with two groups with the 'same number of heads' as opposed to the 'same number of heads and tails.' Tails shouldn't matter.

Anonymous 13 February 2010

The answer to puzzle #7 does not make sense. With 90 tails and 10 heads, forming two sets with equal heads and tails is impossible.

Anonymous 2 March 2010

The logic in number 7 seems flawed. If one set has all tails and the other has a mix of heads and tails, flipping them will not result in matching sets.

Anonymous 22 March 2010

The Flipping Coins problem is unsolvable and the solution is nonsense. Has this been worded incorrectly?

Anonymous 1 December 2010

The solution proposed to 'Flipping Coins' seems incorrect. It should involve separating a group of 10 coins and flipping them to ensure both sets have the same number of heads.

Anonymous 6 December 2010

I've noticed that the solution proposed to 'Flipping Coins' is incorrect, or at least it seems so to me. I know this problem with a bit different conditions: one must create two arbitrary groups of coins with the same number of heads.

Anonymous 6 December 2010

The solution proposed to 'Flipping Coins' seems incorrect. I believe that to create two groups of coins with the same number of heads, one must separate a group of 10 coins and flip them all. This way, the number of heads will be the same as in the remaining set of 90.

Anonymous 27 November 2012

The solution to the Flipping Coins puzzle either does not work, or I don't understand it. If you flip over ten coins, you are not necessarily going to get the same amount of heads and tails as the other pile.

Anonymous 27 November 2012

The solution to 'Flipping Coins' doesn't make sense to me. If you don't know which are heads or tails to begin with, then the selection for each group of 10 is random. There are many possibilities for each group and I don't see how flipping all of the coins in one group will make them the same.

Anonymous 27 November 2012

The Flipping Coins puzzle is incorrectly stated, and your solution doesn't work. If one of my groups has 1 head and 9 tails, and the other has 2 heads and 8 tails, flipping all of one group over will not make them match.

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