First, I noticed that if I arrange all the rods from smallest to largest, each rod is 1 unit longer than the previous rod (please see attached picture).
w= 1 unit, r= 2, g= 3, p= 4, y= 5, d= 6, b= 7, t= 8, B= 9 and o= 10
The train shown in this picture is made of 20 white rods. To find out which other color rods can make this train, I decided to skip-count. If you reach 20 using skip-counting, then that color rod can be used to make the train. The number of times you skip-count tells you how many rods you need to use to make the train. r (2 units long) = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (10 red rods are needed to make the train)
g (3 units long) =3 , 6, 9, 12, 15, 18, 21 (You cannot use the green rod because you don’t get 20 during the skip-count, you can make a train that is 18 units long or 21 units long but not 20 units long)
p (4 units long) = 4, 8, 12, 16, 20 (5 pink rods are needed to make the train)
y (5 units long) = 5, 10, 15, 20 (4 yellow rods are needed to make the train)
d (6 units long) = 6, 12, 18, 24 (Cannot use dark green rods)
b (7 units long) = 7, 14, 21 (Cannot use black rods)
t (8 units long) = 8, 16, 24 (Cannot use tan rods)
B (9 units long) = 9, 18, 27 (Cannot use blue rods)
o (10 units long) = 10, 20 (2 orange rods are needed to make the train)
Red, pink, yellow and orange rods can be used to make the train. When I solved this problem, my brother told me that you can find the factors of 20, which are numbers that can be multiplied to make 20. So, 1, 2, 4, 5 and 10 are factors of 20. By using this strategy, again, red, pink, yellow and orange rods can be used to make the train.