Slow board lately; perhaps this puzzle will spark some interest.
After several hours into the race and lapping others at will, Germany's latest wunderkid Gauss realizes that 1/5 of the racers in front of him plus 5/6 of the racers in back of him add up to the total number of racers.
How many cyclists are there in the race?
[credit: Pierre Berloquin]
Puzzle This
Fri, 03/14/2003 - 10:58am
Fri, 03/14/2003 - 11:40am
#1
Man I got a few people on this at work. Math skills seem to be going away.
Fri, 03/14/2003 - 12:00pm
#2
Popping pills
I'm sure the answer is none as Gaus had just taken an Ecstasy pill and imagined the whole thing.
Fri, 03/14/2003 - 11:24am
#3
riders
no doubt other riders in this peloton include cauchy, smirnov, kolmogorov, poisson and boole.
Fri, 03/14/2003 - 12:13pm
#4
31.
How about this...A man is in a prison with two unmarked doors, one of which leads to freedom, the other to death. Each door has a guard, one of whom always tells the truth, the other always lies. Both guards know which door is which. The prisoner is permitted to ask one question of one of the guards. The guards can give only a yes or no answer. What question should the prisoner ask in order to determine which is the door to freedom?
Fri, 03/14/2003 - 1:31pm
#5
I don't think 31 is the answer. Unfortunately I can't figure it out. I hope someone gets the answer because the guys here at work say it's not possible.
1/5x + 5/6x + 1=x
Or somethinglike that.
Fri, 03/14/2003 - 1:40pm
#6
Somehow 1/5 and 5/6 are greater than 1--a common denom. of 30 yields 31/30 plus the rider himself. But it just doesn't seem to make logical sense.
Fri, 03/14/2003 - 1:48pm
#7
Solution
"Here's the ""masked"" solution. Drag your mouse over the text below while pressing your mouse button if you really want to see it...
--start drag here --
pen n paper way...
(1/5)(n - 1) + (5/6)(n - 1) = n
where n is the number of particpants and the ""- 1"" is to account for Gauss.
Alternatively, the do-it-in-yer--noggin' solution...
1/5 + 5/6 = 31/30
next include Gauss to get a nice clean ratio, 31/31
--end drag here --
Peter"
Fri, 03/14/2003 - 2:33pm
#8
But then your not taking into account the other rider. That's why I couldn't figure it out. You just erased the rider in the middle
Fri, 03/14/2003 - 2:39pm
#9
Yeah it's been racking my brain. It's just not possible. 1/5 + 5/6 = a number greater then the whole and you still need to add the final rider. This is not logicaly possible.
Thanks for wasting my time HAHAHA
Fri, 03/14/2003 - 3:03pm
#10
It's time for a beer :-)
Dude, w/ your last 2 posts, u r so close, like dancing around the perimeter of the bull's eye...
... 1/5 + 5/6 = a number greater then the whole and you still need to add the final rider. ..
It's not whole until you add the final rider.
Fri, 03/14/2003 - 3:18pm
#11
"The key word is 'lapping'. That means every other racer is simultaneously ""in front of"" Gauss and ""in back of"" him. So, if you have 31 racers, 30 are in back of Gauss and the same 30 are also in front of him (assuming none are riding by his side). 1/5 of 30 plus 5/6 of 30 equals 31."
Fri, 03/14/2003 - 1:39pm
#12
2 minuses always make a plus
"Ask one of the guards, ""If I were to ask the other guard if this door leads to freedom. What would be his reply?""
If the reply is ""yes"", then you are a dead man walking. If ""no"", then you are free."
Fri, 03/14/2003 - 3:21pm
#13
Touché.
