26 // The Collatz–Syracuse–Ulam Problem
The only possible normal magic hexagons, of size 1 and 3, and an abnormal hexagon of size 7.
That’s true for ‘normal’ magic hexagons, where the numbers are consecutive integers starting 1, 2, 3, . . . . But it turns out that there are more possibilities if you allow ‘abnormal’ ones, where the numbers remain consecutive but start further along, say 3, 4, 5, . . . . The largest known abnormal magic hexagon was found by Zahray Arsen in 2006. It has size 7, the numbers run from 2 to 128, and the magic constant – the sum of the numbers in any row or slanting line – is 635. Arsen has also discovered abnormal magic hexagons of size 4 and 5. See en.wikipedia.org/wiki/Magic_hexagon
........................................... The Collatz–Syracuse–Ulam Problem Simple questions need not be easy to answer. Here’s a famous example. You can explore it with pencil and paper, or a calculator, but what it does in general baffles even the world’s greatest mathematicians. They think they know the answer, but no one can prove it. It goes like this. Think of a number. Now apply the following rules over and over again: