There are 5 Quisenaire blocks. The first has length 1, the second has length 2, and so on. Each player will be building their own line of blocks, which is initially empty. A move consists of a player adding a single block to their own line. A player continues making moves until their line meets or exceeds the length of the other player's line. The game ends when all blocks have been used. The player with the longest line wins. If both players play perfectly, is it better to go first or second? If you're able to solve this, and it interests you, please generalize for blocks of length {1, 2, ..., n}. I would also be interested in exploring other sets of blocks if it makes the puzzle more interesting.
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$\begingroup$ Seems like each player best strategy is just using the longest block available? Is this what you intended, or are there other rules? Otherwise it's too simple, as first player always wins. $\endgroup$– justhalfApr 18 at 15:43
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1$\begingroup$ @justhalf When it's a player's turn to play they can do any number of moves, but as soon as they match or exceed the other player's line, the turn passes to the other player. The first player's first turn consists of course of only one move since the other line still has length 0. $\endgroup$– Jaap ScherphuisApr 18 at 15:49
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$\begingroup$ @JaapScherphuis, ah, thanks, that's what I missed $\endgroup$– justhalfApr 18 at 16:05
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1 Answer
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With perfect play the winner will be the person who goes
first
We can see that, given that there are 15 units in total, a player just needs at least 8 to win.
If the first player takes the 3, then they would just need the 5 in their second turn to win. Therefore the second player will need to take the 5 block.
There are three ways that the second player can do this, listed below, with the winning response by player 1:
{1,5} -> {2,4}, {2,5} -> {1,4}, {5} -> {1,4}
