Less is more

Use your knowledge of place value to try to win this game. How will you maximise your score?

Age
7 to 11
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Explaining, convincing and proving
Being curious Being collaborative Being resourceful Being resilient

Problem

Less Is More printable sheet

 

The video below introduces this challenge:

 

You can have a go 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 picture below. (The cells on the left don't need to be a different colour, but we will refer to those cells later.) Alternatively, you could print off this sheet of cells.

The first row has 2 blue cells, a 'less than' sign, and 2 white cells. The second row is identical to the first.

Version 1

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 have created four two-digit numbers.

Teams then check if their number sentences are correct:

  • If both number sentences are correct, the team scores the sum of the two two-digit numbers written in the blue boxes.
  • If only the first number sentence is correct, the team scores the two-digit number in the top blue boxes.
  • If only the second number sentence is correct, the team scores the two-digit number in the bottom blue boxes.

The winner is the team with the higher score. See Getting started for some examples of scoring.

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?

In between rounds, teams might like to try to find the highest possible score they could have achieved, if they had known the eight numbers in advance. Their new scores can be added to their running totals.

Will this affect your strategy in the next round?

 

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?

 

Final challenge:

Now, imagine that the numbers 1, 2, 3, 4, 5, 6, 7 and 8 have been thrown.

Where would you place them in order to get the highest possible score? 

Can you provide a convincing argument that you have arranged the numbers in the best possible way?

 

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.

 

An interesting follow-up to this game is More Less is More, which again challenges you to create correct statements, but this time after carrying out some simple calculations.

This activity featured in an NRICH student webinar in November 2022.