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These challenges follow on from Less is More.
This video below introduces these challenges:
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. Our dice 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, have a go at playing the game in a similar way to Version 1, but this time, note down all eight dice rolls before deciding where to place them.
Keep a running total of your scores.
Who is the winner after ten rounds?
Who is the first to reach 500 points?
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.
You may like to check whether you have indeed got the maximum score by typing the numbers 1 to 8 (without commas and with no spaces between them) into the 'Values' box in the Settings of the interactivity above, and then testing your solution.
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?
Follow the clues to find the mystery number.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?