Seeing Rhombuses
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.
Problem
This game is part of a set of three. We recommend you play this version after having a go at Seeing Squares and Seeing Parallelograms.
Seeing Rhombuses printable sheet
Printable dotted grid
This game can be played against a friend or against the computer.
Players take it in turns to click on a dot on the grid - the first player will place blue triangles and the second player will place pink squares.
The winner is the first to have chosen four dots that can be joined to form a rhombus.
Rhombuses can be anywhere and any size.
Clicking on the purple settings cog allows you to select the size of the grid, who the players are, and who goes first.
Once you've played a few times against a friend, you might like to discuss your strategies, and then test them by playing against the computer.
Can you find a winning strategy?
If you are not using the interactive game, you may like to print off some dotty paper.
You may be interested in the other problems in our Strategy Games Feature.
Getting Started
You may want to play Seeing Squares and Seeing Parallelograms before having a go at this game.
Please be aware that there is a special rhombus which you will know by another name...
Here is a collection of rhombuses, one of which is also a square.
Therefore a square is a rhombus.
Student Solutions
Thank you to everybody who sent in their ideas about this game. Most people found that the easiest way to win was by making a square, which is a special type of rhombus, so the solutions are very similar to the solutions for Seeing Squares.
Dhruv at The Glasgow Academy in the UK sent in this image:
Dhruv said:
I decide where to place my dot depending on what the opponent plays. You can beat the computer if it goes first but it is difficult.
Thank you for sharing these ideas with us, Dhruv. I can see lots of ways that you can win from the position in the picture!
William described a similar strategy, and explained where the computer would make its moves:
Place 3 dots in a row on the second line (just below the first line)
The computer will make its move under/on top of the middle shape
Then you have to place your move on the opposite the computer made (up or down the middle dot)
The computer will try to prevent your move by going left or right
You make your move the opposite where the computer made, and you now have a victory.
This is a good strategy - we were also sent similar explanations by Hogan at Banstead Prep School and Sebastian at The British School Al Khubairat in UAE.
We received a few solutions from the children at The British School Al Khubairat. Charlie explained a strategy which relied on making triangles:
I tried many approaches, however, in my most useful method, I tried to create triangles (which I would later make into a rhombus). Making many triangles allows ways you can change your shape to allow the shape of a rhombus.
Can you see the triangles that Charlie has made in this solution? I wonder if there is a way to adapt this strategy to make non-square rhombuses?
Shafin had a similar idea that also involved making triangles:
If you do 1, then 2, then 3, then you will force the computer to go to 6. Then, you should go to 4 so you trap the computer. Finally, go to the remaining dot to win!
Thank you all for sharing these ideas with us.
Teachers' Resources
This game is part of a set of three. We recommend you play this version after having a go at Seeing Squares and Seeing Parallelograms.
The Teachers' Resources for Seeing Squares contain all our suggestions for how these games and interactivities might be used in the classroom.