A girl has $20$ different jewels, she wears $5$ each day. Prove that in $267$ consecutive days, she wore the same pair of jewels on $15$ different days.
How could I approach this? maybe by using the pigeonhole principle?
2026-03-26 02:46:49.1774493209
How to prove that she wore the same pair of jewels on $15$ different days
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Indeed you can use the pigeonhole principle.
Hints:
How many pairs of jewels are there in total?
How many pairs of jewels does she wear each day?
How many pairs of jewels does she wear in $267$ days?
Averaged across the total number of pairs, on how many days does she wear each pair of jewels in the $267$ days?
Can that average be achieved if each pair is worn for $14$ days or fewer?