While organizing my bookshelf, I found an old issue of "Kvant" – a popular Russian science magazine. It has a regular section with entertaining math and physics problems for school students. I post here the part "a" of one problem that I liked:

Each square of an infinite square-ruled sheet has a natural number written in it.

a) Every number appears exactly once.

1) Show an example of such arrangement.

2) Prove that for any number m, there is always at least one pair of neighboring

squares (sharing a side) such that the difference of their numbers is not less than m.

The part "b" of the problem is marked with an "*" meaning it is of higher difficulty. So I am not going to show it here just yet.

Unfortunately, I don't have the issue with the answer to this problem.

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## Prime 15

While organizing my bookshelf, I found an old issue of "Kvant" – a popular Russian science magazine. It has a regular section with entertaining math and physics problems for school students. I post here the part "a" of one problem that I liked:

Each square of an infinite square-ruled sheet has a natural number written in it.

a) Every number appears exactly once.

1) Show an example of such arrangement.

2) Prove that for any number m, there is always at least one pair of neighboring

squares (sharing a side) such that the difference of their numbers is not less than m.

The part "b" of the problem is marked with an "*" meaning it is of higher difficulty. So I am not going to show it here just yet.

Unfortunately, I don't have the issue with the answer to this problem.

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