Donald’s design

In 1982, Donald Preece published a remarkable design (a “double Youden rectangle”) which he had recently constructed. The design is a layout of an ordinary pack of playing cards, with properties described below.

I discussed this design before here.

Donald was so pleased with his design that he stuck playing cards to a thick card and mounted them (with commentary) in a frame, so they could be displayed in the foyer of a mathematics department.

This never happened. But the mathematics building at Queen Mary is being refurbished, and as part of clearing Donald’s papers from the emeritus staff offices, I found the original (which, you will note, is slightly different from the version he published).

Below is a photograph of the design. I have been unable to make the commentary legible, so I have put it in the text around the picture.

A “BALANCED DESIGN”

1. Each value A, 2, 3, …, 10, J, Q, K appears once in each row.
2. Each suit appears in each column.
3. Each pair of the values A, 2, 3, …, 10, J, Q, K occurs together in just one column.
4. Each row has 3 cards of each of 3 suits, and 4 cards of the other suit.

Design obtained by D. A. PREECE (Rothamsted Statistics Department) and published in 1982.

This arrangement of cards is a possible design for an experiment on fruit trees.
Each card corresponds to a “plot” of trees, the plots being in 4 rows and 13 columns.

The values A, 2, 3, …, 10, J, Q, K represent 13 treatments from a first set, and the suits represent 4 treatments from a second set.