There is well known problem:
The picture is attached to a string and you want to hang it on N nails so that if one takes out any of the nails, the picture falls. How do you do it?
For those who have not heard this puzzle:
No brainteaser tricks are here, this is basically topology problem: "How to put N points and a closed curve on a plane in a way that curve can't be moved to infinity without crossing any point, but if one arbitrary point is removed - it can?"
Is it possible to generalise in the following way?:
The picture is attached to a string and you want to hang it on N nails so that if one takes out any M of the N nails, the picture falls, but if one takes out any M-1 nails the picture will not be freed. How do you do it?
Does this problem have a solution? Can it be shown that this is impossible to do if
M > 1?