Here I am, as promised, with the answer to the puzzle I posted last year.
Although only one person has been brave enough to claim she’s solved it, a quick glance at my blog statistics tells me that quite a few others dropped in for a look. Either you worked out the solution but were too exhausted by the effort (or just plain lazy) to blow your trumpets; or else – like me – you didn’t, so you couldn’t.
The problem: using two egg-timers that run on sand, one for four minutes and a larger one that goes for seven, how could you time nine minutes…for a ridiculously over-cooked hen’s egg, or perhaps a giant one laid by an ostrich?
It seemed to me that I could only achieve 8 minutes (2 X 4) or eleven minutes (7 + 4.) But I missed something obvious.
Start both the timers off together. When the four-minute one is empty, turn it over immediately to begin another four minutes. The larger timer still has three minutes to go; let it run its allotted time and turn it over immediately to begin another seven. At this point the smaller timer has run three out of its four minutes. Leave it be.
The smaller timer finishes its second run, having totalled eight minutes, still a minute short of the target. But the larger one has only had time to run for one minute so far. Turn it over and its sand will run back for just one minute till it is empty…total elapsed time nine minutes.
Easy peasy. Then why didn’t I see it for myself?
Karen, I assume you worked it out…well done to your Little Grey Cells. You’re obviously in for a very bright and brainy 2012. Let’s hope the rest of us can catch you up.
I wish everyone a very good New Year, with time for happy reading, especially (of course) plenty of puzzling mysteries.
SEEMS A BIT COMPLICATED, JANE, I THOUGHT OF SETTING THE FIRST TIMER TO RUN HALF-WAY THROUGH IT’S FIRST TWO MINUTES, THEN SET IT ON IT’S SIDE, EFFECTIVELY STOPPING THE FLOW. THEN START THE SECOND TIMER TO RUN IT’S 7 MINUTE COURSE, AFTER WHICH YOU SET THE FIRST TIMER UPRIGHT TO FINISH IT’S OTHER HALF – TWO MINUTES ADDED TO THE SECOND TIMER’S 7 MINUTES GIVES THE REQUIRED 9 MINUTES IN TOTAL.
WELL, OK, MAYBE A GRAIN OF SAND OR TWO OUT, BUT NEAR ENOUGH EH?
HAPPY NEW YEAR!
Obviously, you and your husband are far brighter than I am! :0)
Margaret, that’s a lovely practical solution – your LGC’s are working well! – though I suspect whoever thought up the puzzle wanted just the timers to be used, without human judgment intervening. But your ostrich egg would certainly be cooked! Carol, I can’t claim to have solved it without a very large clue from Richard, who being a mathematician by training is good at this sort of thing.
I admit — I also thought of Margaret’s solution – not the one you posted. It would be enough for anything in my life needing timing!
Nice one, Karen! Even when I got to the “correct” solution, I’d never thought of the one you and Margaret arrived at.
Ah, so I can now throw away the piece of paper here with numbers all over it, interspersed with cryptic instructions to ‘turn over’… thanks for a great puzzle Jane!
Glad you enjoyed it, Ruth, and also glad, in a purely selfish way, that you were baffled – as I was. You’ve made me wonder now – how did the Ancient Romans time their boiled eggs? They certainly ate them, and they’d have had sand timers, but no real idea of “minutes”. I suppose they (or their cooks) experimented till they found a timing that suited everyone, and used that amount of sand in future? Enquiring minds want to know…at least mine does. Ideas, anyone?
A BIT LATE REPLYING TO THIS JANE, BUT DIDN’T THE ROMANS WEAR METAL HELMETS WITH HOLES IN THE TOP – ONE COULD BE SUSPENDED WITH THE APPROPRIATE AMOUNT OF SAND POISED TO DRIBBLE OUT FOR THE PERFECT 3 TO 4 MINUTE EGG.