Problem Teachers' Notes Solution

# Dotty Six

Children at Hythehill Primary sent in some strategies for winning the game:

If there were two sixes in a row, put your dots out of the row.
Start in the centre box.
The person that goes first should put the dots in a corner.

Helen and Molly from Moorfield said:

We think that when you play Dotty Six that you play it with two different coloured pencils and have one each so that you don't get confused.

Many of you sent in your suggestions for changing the rules of the Dotty Six game. Here is a selection of those we received:

Play to $12$ dots in each box, instead of $6$, still with one dice. This means that one person cannot win a box in one go. It also makes the game longer.
Joe and Caitlin from St Michael's
Players have a dice each. They roll at the same time. The person with the highest score on the dice places their dots on the grid. If both players throw the same, the person with the highest score last round places again. Play to $10$ in a box. The game is longer and harder - it's more competitive.
Charlie and Kai from St Michael's
Start by putting a random number of dots (from $0$ to $5$) in each box. Then play as before. This makes the game shorter, but you have to throw an exact number more often.
Seb and Alex from St Michael's
Play with two dice. You can use the scores to calculate a total using addition, subtraction, multiplication and division. $12$ wins a box, but you can place more and then subtract. This is a much more complex version.
Sam and April from St Michael's
Play as before but a line can only be won by winning all three boxes (as in noughts and crosses). This makes the game feel fairer, but can result in a draw.
Molly and Asher from St Michael's
Use a $4$ x $4$ grid and win by winning the fourth box in a line. This makes the game longer. Adding a rule to win a box by getting to $7$ makes it slightly harder still.
Charlotte and Tiger-Lily from St Michael's
Each player will have two boxes, one with the number one in the corner and the other with the number two in. You will also need two dice. In turn, each player rolls both dice and can add, subtract, multiply or divide to make a total. Put this in your first box. Roll both dice again and use add, subtract, multiply or divide to make another total. Put this in your second box. Then the other player has a go. The aim is to get a total of ten in your first box and twenty in your second box. You can add or subtract your numbers to your total in the box. The winner is the first person to get ten in their first box and twenty in their second box.
April from St Michael's
To make the game harder we also think that you should roll two die and $18$ to be the maximum number of dots in a square or have a $16$ square grid.
Helen and Molly from Moorfield
There isn't really a solution to this activity however we are going to share with you some of the ways that it could be adapted. You could make the grid bigger and use a bigger numbered die or play with more people.
Harry and Jack from Moorfield
Another variation of the game could be that each person is not allowed to draw dots on the same row as the person before them. The player who is stuck and cannot do their turn loses!
Karnan from Stag Lane Juniors
We tried lots of variations on the rules
1.You must split the dots into two boxes (this means if you roll $1$ you must miss a turn).
2. Different sized grids eg $4$x$4$, $5$x$5$, $6$x$6$
3. Different totals for the box eg $7$, $9$, $15$
Children at Hythehill Primary

These all sound very good suggestions. Well done!