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Suppose two players are starting this game. Jane owns Blue and Green and Rob owns Yellow and Red. After tossing a coin, Jane gets the first turn. As well as wanting to get her squares filled, Jane wants to make it difficult for Rob.
She notices that in the Yellow Square, Rob already has only four places in which to put a 9 - can't be the top row or the right hand column. If she put a 9 in the middle row of Blue he would then be restricted even more - he could then only put his 9 in one of two squares in the bottom row of Yellow.
Alternatively she could note that Rob's choices for placing 4 in the Red square are limited to only four squares (excluding the bottom row and right hand column). Jane could restrict his choices further by placing a 4 in the middle column of Blue or the middle row of Green.
When Rob has his turn, he might decide to limit Jane's options in Blue by placing a 7 in the left hand column of red or the middle row of Yellow.
As the game proceeds, both players will find that their options for placing their numbers become very restricted. It is very likely that at least one of them will have to use turns to take one or more of their numbers out and replace them to free up spaces for the numbers they still have to place. Winning the game usually depends on having successfully blocked your opponent at some stage.
Being a little cunning right from the beginning is the only way to win!