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Given 2 bags and 5 stones, how would you place the stones into the bags so that the following three conditions are met:

Both bags contain an odd number of stones.
Every stone is inside a bag.
The bags and the stones can not be damaged in any way.

Bonus question: Same as above except both bags contain an even number of stones.

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!

Full disclosure: I can’t remember if I created the “odd” version of this puzzle as I have known about it for at least 4 years. I am pretty certain that I created the bonus “even” version of this puzzle.

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    $\begingroup$ +1 for giving users with less reputation a chance to answer $\endgroup$
    – Blue Herring
    Commented Oct 17, 2023 at 13:30
  • $\begingroup$ The "odd" version has been around in various forms for quite some time. $\endgroup$
    – Daniel Mathias
    Commented Oct 17, 2023 at 13:59
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    $\begingroup$ Is there such a thing as a stone bag? $\endgroup$
    – Florian F
    Commented Oct 18, 2023 at 11:52
  • $\begingroup$ @FlorianF +1 Stone bag - what a cool idea! Maybe someone will make a puzzle about putting bags into stones. $\endgroup$
    – Will.Octagon.Gibson
    Commented Oct 18, 2023 at 19:04

3 Answers 3

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The main problem can be answered by

placing all the stones in bag "A", then placing bag "A" into bag "B". Both bags now contain five stones.

The bonus question can be somewhat neatly solved by

placing three stones into bag "A", the other two into bag "B", then placing bag "B" partially into bag "A", in such a way that only one of the stones inside are also inside bag "A".

Solution done with real bags and "stones":

Five stones in two bags

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  • $\begingroup$ Those are fun stones. Are they anything in particular? They look like game pieces $\endgroup$
    – Chowlett
    Commented Oct 18, 2023 at 22:04
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    $\begingroup$ @Chowlett They are sub-cubes of a dismantled Rubik's Cube: four vertexs and one side, if I'm not wrong. $\endgroup$
    – dr_
    Commented Oct 19, 2023 at 7:20
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Numbering the stones 1-5 and denoting the bags with {} and [] the stones can be arranged as follows:

{[1],2,3,4,5}

to solve the main problem (1 stone in the square brackets bag, 5 in the curly one).

The bonus is trickier, I've got two potential solutions but neither feel satisfactory.

The definitely cheating option:

{1,2},[3,4,5]

and claim that the square bracket bag contains 2 stones (as well as containing 3).

The bag abuse option:

{1,[2},3,4,5]

requires one stone to be shared by two bags without one bag being contained in another. This could reasonably be done with drawstring bags, but it feels pretty dubious.

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This feels slightly cheaty but:

Call the two bags "Bag A" and "Bag B". Put 3 stones in Bag A and the other two in Bag B. Then put bag Bag A in Bag B. Bag A will have the 3 stones we placed in it. Bag B will have the 2 stones we placed in it plus the 3 from Bag A, so 5 in total. Thus each bag has an odd number of stones in it.

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