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Have You Got It?

Can you explain the strategy for winning this game with any target?

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The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.

Yih or Luk Tsut K'i or Three Men's Morris

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.

Nim-7

Age 5 to 14
Challenge Level

We had some great ideas sent in for this task, so thank you to everybody who sent us their solutions.

Lots of children noticed that if there are three counters left at the beginning of your go, you can't win. Josh, Arthur and Mia from Kirkby on Bain in the UK said:

We have noticed that when there are three counters left no matter what the next player takes, the other player will win. This is because there will be one left if two are taken, and two left if one is taken. So the other player will win!

Josh, Arthur and Mia then explained how the first player could win:

Player 1 should take one counter as their first go. This means they will get to leave three counters after their second go and then win. We are going to try with 9 counters!

Thank you for sending in these ideas. I wonder what the best strategy for winning is with nine counters?

We also had lots of ideas sent in from the children at St Charles Primary School Ryde in Australia. Samuel suggested that if there are seven counters left, you should take one counter so that there are six left. Can you definitely win if you leave six counters for the other player? Why?

The children from Olga Primary School in the UK sent in lots of videos explaining their ideas. Francis and Caitlin explained why leaving three counters for the other player is a winning strategy:

Ben and Ayaan explained why going first means you can always win:

Thank you all for sending in your thoughts about this game!

Thank you as well to Eloan and Ella from Clifton College Prep School in England, Joshua from Spring Hill Primary School in Australia, the children from Waverley Primary School in the UK, and Dhruv from Pict in India, who all had similar strategies.