Ginger has 12 plastic bead containers. The containers measure 1 inch on each side. How many rectangular prisms, each with a different-sized base, could Ginger make by stacking all of the bead containers?

Number of different bases for each one:
1 1 12 --->1 1 12, 1 12, 1 2 of them
1 2 6 ---> 1 2 6, 1 6, 2, 2 6 1 --- 3 of them
1 3 4 ---> 1 3 4, 1 4 3, 3 4 1 --- 3 of them
2 2 3 ---> 2 2 3, 2 3 2 2 of them
Answer-10 different prisms

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)