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Pros and Cons
If p is a positive integer and q is a negative integer, which of these expressions is the greatest?
Connect Three
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
Minus One Two Three
Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?
Age 14 to 18
Challenge Level
You may also wish to explore Gathering Gems and Diamond Collector, two similar games which use compass directions and straight line graphs instead of vectors.
In the game below, twenty gems have been placed on a grid.
You start at your home at the origin, and can specify up to eight vectors that describe a path. Any gem that lies on one of your vectors counts towards your total!
But be careful - your final vector must bring you back home again or all the gems will be lost.
Once you have explored the first level, you can challenge yourself to some harder arrangements of gems in Levels 2 and 3 using the Settings menu - just click on the purple cog in the top right corner.
In the game below, twenty gems have been placed on a grid.
You start at your home at the origin, and can specify up to eight vectors that describe a path. Any gem that lies on one of your vectors counts towards your total!
But be careful - your final vector must bring you back home again or all the gems will be lost.
Once you have explored the first level, you can challenge yourself to some harder arrangements of gems in Levels 2 and 3 using the Settings menu - just click on the purple cog in the top right corner.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.