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By drawing $9$ lines, $5$ horizontal and $4$ vertical, one can form $12$ small rectangles, as shown on the right. What is the greatest possible number of small rectangles that one can form by drawing $15$ lines, either horizontal or vertical?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
How Many Rectangles?
Age 11 to 14
ShortChallenge Level 
By drawing $9$ lines, $5$ horizontal and $4$ vertical, one can form $12$ small rectangles, as shown on the right. What is the greatest possible number of small rectangles that one can form by drawing $15$ lines, either horizontal or vertical?If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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