how many ways each total can come up — and how to count them without a table
Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.
Three sizes in one archive — from a sheet on the fridge to a poster on the wall.
The count is for fair dice that fall independently. Pairs are ordered: 1-6 and 6-1 are two different throws, which is why a row shows both.
With three dice, 9 and 10 can each be made from 6 sets: 9 is 1+2+6, 1+3+5, 1+4+4, 2+2+5, 2+3+4, 3+3+3; 10 is 1+3+6, 1+4+5, 2+2+6, 2+3+5, 2+4+4, 3+3+4.
But a set of three different numbers can come up in six different orders, a set with a pair in three, and three of a kind in only one. So 10 comes up 27 times in 216 and 9 only 25; the same goes for 11 and 12. Galileo explained exactly this: in his words, players had long held 10 and 11 to be better than 9 and 12, although all four can be made from the same number of sets.
Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 7 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.
the IWF colour code and the plate count: from target weight to each side of the bar, no calculator
why a “yes” from a test that is right 99 times in 100 is wrong more than nine times in ten when one in a thousand has the thing
the first digit of a number: why a one turns up more than six times as often as a nine, and in which sets that is true
how many people it takes for two of them to share a birthday — and the same count for codes and fingerprints