This is an attempt to explain what is going on without using any maths... I'll get around to a mathematical description Real Soon Now! -- Rob. ------------------------------------------------------------------------------ OK. Imagine a lake with lots of stepping-stones (actually they are points on an elliptic curve and there are 416363315556124458285894983 of them). There is a sign on each stone indicating which stone to step to next (actually there is a function, it doesn't really matter which one, just that it is fairly random and fixed in advance.) There are about 50 of us who each parachuted in to a random stone and started following the signs, stepping from one stone to the next a few tens or hundreds of thousands of times per second. Every billion steps or so we find a stone which is "distinguished" in some way, for instance it is particularly small, and before leaving it we paint a mark on it indicating that we have been there (actually we send some info about it to a central site by email). After something like 30000 billion steps, one of us will step on a stone that another of us has already visited. He'll continue following the signs, just as the previous visitor did, and after a while will find a stone that they painted a mark on. Then we'll know that two of us have stepped on that stone and using some information the two people recorded about the paths they took, we can calculate the final answer. ------------------------------------------------------------------------------ We are not sure exactly how many steps will be necessary because of the randomisation but we can estimate how many. The table below contains two columns: if at some stage we have marked the number of stones indicated in the left column but have not found the answer yet, then the expected number of stones left to mark before we finish is given in right column. Initially none were marked and we expected 30000 in total. As I write this we have done 20000 (NB: there is an up-to-date total in counter.text at the Web site). Reading from the table, we expect about 16056 more. At a rate of 1200 per day, this should take two weeks. Note that 16056 is more than 30000 minus 20000 because we have to take into account the fact that in theory we could have found the answer already, but in fact that wasn't the case. ------------------------------------------------------------------------------ Done : Expected remaining ==== ================== 0 : 30000 <- we started here on the 18th of December. 1000 : 29017 2000 : 28067 3000 : 27150 4000 : 26265 5000 : 25414 6000 : 24594 7000 : 23806 8000 : 23048 9000 : 22321 10000 : 21623 <- we were here on the 29th. 11000 : 20953 12000 : 20311 13000 : 19696 14000 : 19106 15000 : 18541 16000 : 18000 17000 : 17482 18000 : 16986 19000 : 16511 20000 : 16056 <- we reached here on the 6th of January. 21000 : 15620 22000 : 15202 23000 : 14802 24000 : 14419 25000 : 14051 26000 : 13699 27000 : 13361 28000 : 13037 29000 : 12725 30000 : 12426 31000 : 12139 32000 : 11863 33000 : 11598 34000 : 11343 35000 : 11098 36000 : 10861 37000 : 10634 38000 : 10415 39000 : 10204 40000 : 10000 41000 : 9804 42000 : 9614 43000 : 9431 44000 : 9254 45000 : 9083 46000 : 8918 47000 : 8758 48000 : 8604 49000 : 8454 50000 : 8310 51000 : 8169 52000 : 8033 53000 : 7902 54000 : 7774 55000 : 7650 56000 : 7530 57000 : 7413 58000 : 7299 59000 : 7189 60000 : 7082 <- hopefully we'll never get down here! ------------------------------------------------------------------------------