
Janet's trays
Janet is making trays for an experiment by fitting glass squares into a frame. She uses 8 squares for each tray, 6 clear ones and 2 red ones. The trays can be stacked on top of each other and rotated (180 degrees) but not flipped. She deided to make many different designs as she ca. To help her sort there, she gives each design a code name consisting of two numbers which indicate where the red tiles are placed. (2:8 is the same as 1:7).
If two equivalent designs have different names but Janet doesn't want to distinguish them, then she chooses to call both of them by the name that is smaller when read as a 2digit number. So tray 2:8 is called 1:7
Janet's friend, Tom made trays using 6 squares, 2 red and 4 clear arranged in a 2x3 rectangle. He made all the nine possible designs and named them the way Janet did. He placed them in three stacks wth three trays in each stack.
If trays 1:2 and 1:6 were in different stacks and, when each of these stacks were viewed from above, there was a red square in each of the 6 spaces.
Questions
1. Explain why there is only one possible pair of trays in the stack with 1:6 and only two possible pairs of trays in the stack with 1:2
2. Show that Tom could not have stacked his nine trays into three stacks of three trays each so that there was a read square in each of the six spaces when each stack was viewed from above