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Korea Junior Mathematics Olympiad
2022 Korea Junior Math Olympiad
7
7
Part of
2022 Korea Junior Math Olympiad
Problems
(1)
Move all cards to one deck
Source: kjmo 2022 P7
10/29/2022
Consider
n
n
n
cards with marked numbers
1
1
1
through
n
n
n
. No number have repeted, namely, each number has marked exactly at one card. They are distributed on
n
n
n
boxes so that each box contains exactly one card initially. We want to move all the cards into one box all together according to the following instructions The instruction: Choose an integer
k
(
1
≤
k
≤
n
)
k(1\le k\le n)
k
(
1
≤
k
≤
n
)
, and move a card with number
k
k
k
to the other box such that sum of the number of the card in that box is multiple of
k
k
k
. Find all positive integer
n
n
n
so that there exists a way to gather all the cards in one box.Thanks to @scnwust for correcting wrong translation.
combinatorics