: During the school year, wanting to have some idea of what a million really is, I actually counted to a million, mentally, one number at a time, in off minutes.  Kept a piece of paper in my pocket to mark down the last number when I had to quite. Took me about a week, as I remember.  A million is a lot.

cloister responded:

no way! a million really _is_ a lot; i disbelieve that you could actually count to one million, by ones, in only a week.   first off, one million seconds is approximately 11 and a half days.  so for you to have counted to a million in only seven days, you would have to spend the full seven days, 24x7, awake, counting continuously at about 1.65 numbers per second.   by mentally saying the numbers in full, i can go at about 1.5 numbers per second, and that's only for four digit numbers.   as the numbers get larger and larger, this rate would naturally drop.   but let's be generous and give you the whole 1.5 numbers per second for the full million.  that gives you 7.7 days to do the whole job, assuming you don't stop to sleep or pee or anything like that.   but of course you did need to sleep, etc., so let's figure you really got in, at most, about 10 hours of vigorous counting. at that rate, it'll take you 18.5 days to do the whole million.

the only way i can conceive that you might possibly have pulled such a thing off is if you were cutting corners in your counting by not actually mentally iterating all the digits in each number.   if you just kept a mental note of the high-order digits, and simply rattled off the last two digits in rapid-fire procession, then maybe you could have done it. that is, rather than saying to yourself "one thousand two hundred and one, one thousand two hundred and two, ..." you'd shorten it to "one thousand two hundred and one, two, three, four, ..., ninety nine, one thousand three hundred, ..."   if we let you get away with that shortcut, you can do much better, even if you stop for sleep. a quick experiment shows that by cutting corners as described above, i can count about five numbers per second. this gives us: 1,000,000 numbers / 5 numbers-per-second / 3600 seconds-per-hour / 10 hours-per-day = 5.55 days.

so, i guess it's a judgement call as to whether cutting corners like that really counts as having "counted to a million", even if you could do it in a week.

!! writing myself a reminder to NEVER post anything containing numbers... 
if cloister doesn't get me, Joshua will !!  \(^.^)/