Half and Half
Two of the four small triangles are to be painted black. In how many ways can this be done?
Age
11 to 14
Challenge level
Problem
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If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 6
Here are two possible ways of thinking about this problem, although there are many other possibilities.
Choosing the colour of the top triangle
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$6$ possibilities.
Choosing which triangles are black
If the top triangle is painted black, there are three choices for the other black triangle.
Choosing which triangles are black
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This means there are $3+2+1=6$ possibilities.
This problem is looking at the number of ways to choose two of the four triangles to paint black. This can be written as $^4C_2$ or $4 \choose 2$, which are called binomial coefficiants. If you want to find out more about these, then you can look at this article.