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Kayan from St. Martins School wrote:
I think the rules are:
1) You pick any target number.
2) Place your counter on a starting node and write down its number. This is your current total.
3) Move the counter to any node which is connected to the current node by a line (except the node you just came from). Add the number of the node we move on to, to our current total.
4) Keep going until you reach your target number.
5) The winner is the player who can reach their target in the fewest moves
I think the best way to win is:
1) If our target is 6 or less, start on the node whose number is equal to our target, otherwise start on the node labelled 6.
2) If our target minus our current number is less than 6 then move to the node that gets to our target if possible, otherwise move to the node with the highest number which keeps you below the target.
3) If our target minus our current number is 6 or more then move to the highest numbered node which we are allowed to move to.
3M from the British International School in Ho Chi Minh City, Vietnam sent in the following:
We added a rule that you could not go back to the number that your opponent had just moved from.
Here are 3M's tips for winning at Totality:
1) Do not just keep the total 'running' score, make sure you think about how many more points are needed to win.
2) As you get close to the target number, it is more important to plan a route and think about what the possibilities are. When the total is 11 or less (11 is the largest total you can make in two moves) you have to be really careful.
3) The centre provides more options for moves:
- There are six possible moves when you are in the centre of the board, but only three or four possible moves when you are at the edge.
- Try to put your opponent in a 'dead end' - trapped at the edge of the board - especially at the end of the game. But be careful that you do not end up trapping yourself!
4) Use the zeros to avoid increasing the total and 'skip' your turn, and maybe force your opponent to go over the target number.
These are very clear submissions so thank you all!
Totality
Age 5 to 11
Challenge Level 
Kayan from St. Martins School wrote:
I think the rules are:
1) You pick any target number.
2) Place your counter on a starting node and write down its number. This is your current total.
3) Move the counter to any node which is connected to the current node by a line (except the node you just came from). Add the number of the node we move on to, to our current total.
4) Keep going until you reach your target number.
5) The winner is the player who can reach their target in the fewest moves
I think the best way to win is:
1) If our target is 6 or less, start on the node whose number is equal to our target, otherwise start on the node labelled 6.
2) If our target minus our current number is less than 6 then move to the node that gets to our target if possible, otherwise move to the node with the highest number which keeps you below the target.
3) If our target minus our current number is 6 or more then move to the highest numbered node which we are allowed to move to.
3M from the British International School in Ho Chi Minh City, Vietnam sent in the following:
We added a rule that you could not go back to the number that your opponent had just moved from.
Here are 3M's tips for winning at Totality:
1) Do not just keep the total 'running' score, make sure you think about how many more points are needed to win.
2) As you get close to the target number, it is more important to plan a route and think about what the possibilities are. When the total is 11 or less (11 is the largest total you can make in two moves) you have to be really careful.
3) The centre provides more options for moves:
- There are six possible moves when you are in the centre of the board, but only three or four possible moves when you are at the edge.
- Try to put your opponent in a 'dead end' - trapped at the edge of the board - especially at the end of the game. But be careful that you do not end up trapping yourself!
4) Use the zeros to avoid increasing the total and 'skip' your turn, and maybe force your opponent to go over the target number.
These are very clear submissions so thank you all!
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