perplexus.info :: General : 2001 Coin Crossed 1-2-3 Value Conclusion

2001 Coin Crossed 1-2-3 Value Conclusion (Posted on 2023-05-07)

Each of 2001 coins are assigned the value 1, 2, or 3 and they are arranged in a row.
• Between any two coins assigned the value of 1, there is at least one coin.
• Between any two coins assigned the value of 2, there are at least two coins.
• Between any two coins assigned the value of 3, there are at least three coins.

Determine the maximum number of coins, assigned the value of 3, that could be in the row.

*** Adapted from a problem appearing in a Russian Mathematical Olympiad.

See The Solution Submitted by K Sengupta

Rating: 3.0000 (1 votes)

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Simple (spoiler)

| Comment 1 of 3

There can be 501 coins assigned the value of 3.

501 is clearly the upper bound, based on the third limitation ("between any two coins assigned the value of 3 there are at least 3 coins').

And it is achievable as follows:

The block 3121 is repeated 500 times and then a 3 is the 2001st coin.

This maximum row is then 312131213..3 and all conditions are satisfied.

Posted by Steve Herman on 2023-05-07 07:27:48

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