Tuppins
(page 49)

(Fall 2007) Here's a solution from Tylar Boskey, Jessica Wright, Cody Urlwin, Brett Whitfield, and Trap Yip, from Mrs. Westbrook’s 3rd block class, Northgate High School, Newnan, Georgia. But read on, because there's a controversy...

#### Scenario 1

 XXXXXXXX Player 1: takes the middle two blocks XXX..XXX Player 2: takes either one of the underlined blocks X....XXX Player 1: takes the block that is in the middle of the group of three. X....X.X This is what you should be left with if you followed the steps correctly for this scenario.

#### Scenario 2

 XXXXXXXX Player 1: takes the middle two blocks XXX..XXX Player 2: takes either one of the underlined blocks XXX...XX Player 1: takes the block that is on the end of the group of three. XX....XX Player 2: takes the underlined block. X.....XX Player 1: takes the two blocks on the right. Player 2 is left with only one block, so player 1 wins.

This is what you should be left with for this scenario.

#### SCENARIO 3

 XXXXXXXX Player 1: takes the middle two blocks XXX..XXX Player 2: takes either one of the underlined blocks XXX..X.X Player 1: takes the block that is in the middle of the group of three. X..X...X Player 2: no matter which block they take, they lose.

This is what you should be left with for this scenario.

Our theory is that if the first player takes the middle two blocks on the first move they will always win. This theory works if the player concentrates and plays the game correctly, the purpose of our theory is to leave the other player on his/her turn with three separated block four in a row and they are doomed.

Above are some scenarios that support our theory.

Woo-hoo! Another first solution!

It's hard to figure out how to write up a strategy. I think this is a pretty good job! Readers, what do you think? They have left some things out. Is that OK? Would it make it too long and hard to read to put in every little bit?

For example, at the end of scenario 3, when they say, “no matter which block they take they lose,” should they elaborate and explain why Player 2 is doomed?

Next, I wonder if there is any other reliable way to win.

Finally, I challenge the authors (or anybody else) to find the mistake in Scenario 3 :)

We are Brittni, James, and Jessica, 3 eighth graders from West Virginia.

We found the mistake in Scenario 3:

 XXXXXXXX Player 1: takes the middle two blocks XXX..XXX Player 2: takes either one of the underlined blocks XXX..X.X Player 1: takes the block that is in the middle of the group of three. X..X...X Player 2: no matter which block they take they lose (WRONG)

If you take the middle block out of 5 that are left, it would leave 4 blocks, not 3. Making this move would make Player 1 lose.
X.X..X.X

To which eeps responds:

Bravo! Thanks!

WAIT! But their whole theory is that Player 1 wins by taking the middle two blocks. Now, in Scenario Three, the result is that Player 1 loses.

So if you're player one and take the middle two, I should take the middle one of one set of three.

You -- player one -- are left with this:

X.X..XXX

If you take the middle one of three right now, you lose, right?
Does that change the overall result (that is, would you rather be Player 2?)
OR is there a better move for Player 1?

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