Math Is Fun Forum

salem_ohio

Member

Registered: 2016-03-11

Posts: 37

Guess the coins

Two friends, Alexander and Byron, play the following game: they have 10 coins in a row in front of them and Alexander secretly selects two consecutive coins. Byron defines two subsets of the 10 coins which he presents to Alexander. Then Alexander tells Byron how many of the coins that he chose belong in each of the two subsets (for example, 2 coins in the 1st subset and none in the 2nd). Then Byron must guess, only by one attempt, the two coins that Alexander selected. Find a strategy such that Byron always wins.

Last edited by salem_ohio (2016-03-30 22:31:49)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

Must the cardinality of the 2 subsets equal 10?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

salem_ohio

Member

Registered: 2016-03-11

Posts: 37

Re: Guess the coins

Not necessarily

Must the cardinality of the 2 subsets equal 10?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

Okay thanks.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

Cannot even imagine any solution!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

If I understand correctly choosing two subsets will split the 10 numbers into 3 pieces. Is that correct?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

The two subsets plus the ones not belonging to any of the two subsets. Right.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

I have been unable to find a single solution. I will continue to work on it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

Very intriguing puzzle though!

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

Bobby, now that I think of it, the subsets can also be overlapping. I think that I am close to something...

If I understand correctly choosing two subsets will split the 10 numbers into 3 pieces. Is that correct?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

Overlapping? I do not understand.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

I mean that the two subsets may also have some common numbers.

Overlapping? I do not understand.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

That changes things a lot.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

This is just my guess, maybe we must wait for Salem to confirm But it doesn't say "two different subsets"!

That changes things a lot.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

I do not see how having duplicates in the subsets is going to help anyway. What is needed is more subsets.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

OK, so:
Let's name the coins 1 to 10. We have 9 possible coin sets to guess: 1-2, 2-3, 3-4, 4-5, 5-6, 6-7, 7-8, 8-9 and 9-10.
All possible answers that Alexander can give are 0, 1 and 2 (coins) for each subset, thus 9 possible combinations.
Let's take these two subsets for example: A: {3,4,5,9,10} and B: {5,7,8,9,10}.
Below we list Alexander's replies for each subset A - B and the set of numbers that Byron guesses:
A     B
0    0 ----->1,2
0    1 ----->6,7
0    2 ----->7,8
1    0 ----->2,3
1    1 ----->5,6
1    2 ----->8,9
2    0 ----->3,4
2    1 ----->4,5
2    2 ----->9,10

So this way Byron can always win, no matter which pair of number Alexander has put in mind.

Last edited by anna_gg (2016-04-09 09:24:31)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

What happens if Alexander says (1,1) when he has picked 9,10?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anna_gg

Member

Registered: 2012-01-10

Posts: 232

Re: Guess the coins

then he would have said 2,2 because both numbers (9,10) are in both subsets.

What happens if Alexander says (1,1) when he has picked 9,10?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Guess the coins

Hi;

I misunderstood the problem and that was a good reason why I could not solve it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.