Supercells

A row of cells holds numbers, and some cells are coloured. A cell is coloured when its number is larger than the numbers in the cells next to it. Such a cell is a supercell: like a child who is taller than both neighbours.

In the book's row, 626 sits between 577 and 345. It is larger than both, so it is a supercell. 200 is not, because its neighbour 577 is larger. A cell at the end of a row has only one neighbour: 198 is at the end, next to 109, and is larger, so it is a supercell.

The game works in a grid too: think of a classroom with rows and columns of desks. Now a cell's neighbours are the cells just left, right, above and below it. In the book's Table 1, 8632 is larger than all its neighbours (4580, 8280, 4795 and 1944), so it is a supercell.

When no number is repeated, some things are always true:

• The largest number is larger than everything, so it is always a supercell.
• The smallest number is smaller than all its neighbours, so it is never a supercell.
• Two cells next to each other can never both be supercells, because each would have to be larger than the other.

So in a row of 9 cells, the most supercells possible is 5: the 1st, 3rd, 5th, 7th and 9th cells, with every other cell in between.