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Making Trains

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Rukmini who goes to Dowanhill Primary sent us a very detailed solution to this problem - well done Rukmini!

I counted how many white rods would fit in Laura's train. Her train was 12 white rods long since it had 7 + 2 + 3 = 12. Yes, I can make trains with 3 different colours, of length 12.
First I took the longest rod Orange (10) but I couldn't do it.
I tried each size one after the other.
I could make the following 8 trains:
Blue + red + white = 9 + 2 + 1 = 12
Brown + white + green = 8+ 1 + 3 = 12
Black + pink + white = 7 + 4 + 1 = 12
Black + green + red = 7 + 3 + 2 = 12
Dark green + yellow + white = 6 + 5 + 1 = 12
Dark green + pink + red = 6 + 4 + 2 = 12
Yellow + dark green + white = 5 + 6 + 1 = 12
Yellow + pink + green = 5 + 4 + 3 = 12

In fact, the fourth one in your list, Rukmini, is the same as Laura's and the fifth and seventh are the same, I think. Do you agree?

After that I did not need to check as the same things would be repeated. That is we would get a train like green + brown + white which is the same as brown + white + green.
The train yellow + dark green + white was 12 long and did not use the same colours as Laura, but was just as long.
Rob's train could have been: 6 + 1 + 2 +3 = 12 : dark green + white + red + green or 5 + 1 + 2 + 4 = 12: yellow + white + red + pink
Charlene's train had the 4 shortest rods: 1 + 2 + 3 +4 = 10. Orange rod is of the same length, 10.
Ben's train was 7 + 7 + 3 = 17 long.
He might have made: pink + yellow + dark green + red = 4 + 5 + 6 + 2 = 17
green + brown + pink + red = 3 + 8 + 4 + 2 = 17
green + black + yellow + red = 3 + 7 + 5 + 2 = 17