A child is arranging green blocks in groups of 3 and purple blocks in groups of 6. If she has the same number of green and purple blocks, what is the smallest number of each colour that she could have?

Tamanna is arranging black marbles in groups of 13 and purple marbles in groups of 25. If she has the same number of black and purple marbles, what is the smallest number of marbles of each colour that she could have?

Bobby tutors students in groups of 8. Meanwhile, Polly tutors students in groups of 12. While discussing their work, the tutors realize that they both work with the same total number of students. What is the smallest number of students each can have?

(a) A company that makes crayons is trying to decide which 5 colors to include in a promotional mini-box of 5 crayons. The company can choose the 5 mini-box colors from its collection of 70 colors. How many mini-boxes are possible?

A kangaroo has a large collection of small 1 × 1 × 1 cubes. Each cube is painted one color. The kangaroo wants to construct a cube using 27 small cubes in such a way that any two small cubes sharing a vertex are of different colors. At least how many different colors must the kangaroo use?

In how many different ways can 3 identical green shirts and 3 identical red shirts be distributed among 6 children such that each child receives a shirt