More Less Is More

More Less is More printable sheet - game instructions
More Less is More printable sheet - blank grids

These games follow on from Less is More. 

The video below introduces this challenge:

You can have a go at the four different versions using this interactivity:

If you are working away from a computer, you could treat this as a game for two people, or play in two teams of two.

You will need a 1-6 or 0-9 dice. The interactivity can be used to simulate throwing different dice.

Each team should draw some cells that look like the pictures below.

In Version 1, you place the numbers after each throw of the dice.

In Version 2, you note down all eight dice rolls before deciding where to place them.

Have a go at playing the game and keep a running total of your scores.

Who is the winner after ten rounds?
Who is the first to reach 500 points?
 

Sum-sum

Take-take

Take-sum

Sum-take

Final challenge:

Imagine that you have thrown the numbers 1-8.
What is the highest possible score for each of the games above?
Can you provide a convincing argument that you have got the highest possible score?
A clue is given in the hints.