More less is more
In each of these games, you will need a little bit of luck and your knowledge of place value to develop a winning strategy.
Problem
More Less is More printable sheet - game instructions
More Less is More printable sheet - blank grids
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.
You will need to throw the dice eight times in total. After each throw of the dice, each team decides which of their cells to place that number in.
When all the cells are full, each team will be able to check if their number sentence is correct.
In all cases, you score if the sentence is correct. The score is the result of the calculation on the left of the inequality sign. See Getting started for some examples of scoring.
The winner is the team with the higher score.
In between rounds, teams might try to find the highest possible score they could have achieved, if they had known the eight numbers in advance. Their new scores could be added to their running totals.
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?
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 Getting started.
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.
Getting Started
Sum-sum
Score = 42 + 16 = 58
With 1-8, the maximum score is more than 130 points
Take-take
Score = 55 - 35 = 20
With 1-8, the maximum score is more than 55 points
Take-sum
Score = 42 - 16 = 26
With 1-8, the maximum score is more than 70 points
Sum-take
Score = 12 + 24 = 36
With 1-8, the maximum score is more than 70 points
Teachers' Resources
This problem follows on from Less is More.
See the Teachers' Resources of Less Is More for guidance on how this problem could be used in the classroom.
This problem featured in the NRICH Primary and Secondary webinar in November 2022, and in an NRICH student webinar in the same month.
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