Hello MathFunsters, I've seen this on "Le Monde" webpage. http://bit.ly/12RaSEi Draw a 3x3 square and write "1" in the upper left corner-square. Fill now one by one the other squares according to these rules: - select an empty square - write in it the sum of its neighboring squares (a "corner-square" has 3 neighbours, an "edge-square" 5 and the "center-square" 8) - when all squares are marked, record the highest written value. Example: +-----+-----+-----+ | 1 | | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | | | | | | +-----+-----+-----+ | | | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | | | | | | +-----+-----+-----+ | | 2 | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | 6 | | | | | +-----+-----+-----+ | | | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | 6 | | | | | +-----+-----+-----+ | | 8 | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | | 2 | 6 | | | | | +-----+-----+-----+ | 10 | 8 | 0 | | | | | +-----+-----+-----+ +-----+-----+-----+ | 1 | 1 | 3 | | | | | +-----+-----+-----+ | 22 | 2 | 6 | <--- MAX value = 22 | | | | +-----+-----+-----+ | 10 | 8 | 0 | | | | | +-----+-----+-----+ My best MAX is 40: is it the highest possible MAX in a 3x3 square? What are, if we consider all nxn squares, the MAX values for the first n? The sequence of such MAX starts with S(max) = 1,4,... then what? This is perhaps old hat, sorry -- but there are too many seqs in the OEIS that start with 1,4,... Best, E.