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'Same Length Trains' printed from http://nrich.maths.org/
Thank you for your responses to this problem. Particularly good explanations were sent from Danny who goes to High Ash School, Shubha from Northveil Elementary and Abhijit from Bhavans School. Danny said:
First, we counted how many squares made up the train. $20$.
Then we worked out that we could use $10$ red rods, each of length $2$, to make a train of length $20$.
Then we used $5$ pink rods each of length $4$.
Then $4$ yellow rods each of length $5$.
Then $2$ orange rods each of length $10$.
Shubha gave a little bit more detail:
You have to look at the multiplication tables for the numbers $1$ through $10$.
Find all the combinations that have an answer of $20$. They are $1 \times 20$ = $20$; $2 \times 10$ = $20$; $4 \times 5$ = $20$; $5 \times 4$ = $20$; $10 \times 2$ = $20$
This means that by using the following combinations we can make the train length to be $20$ blocks:
$20$ rods that have a length of $1$ block
$10$ rods that have a length of $2$ blocks
$5$ rods that have a length of $4$ blocks
$4$ rods that have a length of $5$ blocks
$2$ rods that have a length of $10$ blocks
So it means that you can only make $5$ different trains of the same length as Matt's train.
(The first train you mention, Shubha, has already been made by Katie in the question, so there are four others as Danny concluded.) Well done to you all.