if you just add them... and compare that to the sum of the first N integers... which, i think is [n(n+1)]/2... the difference between the two should be your missing number...
1 .. N
Summed = N(N+1)/2
Take N(N+1)/2 and subtract the summation of the random order numbers. There is your answer.
**EDIT**
Doh too late.
just remembered a good one... it's very contrived/constrained (as most riddles are), but is pretty good:
you are running a very dangerous nuclear experiment. you are trying out a new form of putty-like control rods that are supposed to be much cheaper and more effective, but they become ineffective after exactly ten minutes in water and must be replaced. you have two types of rods: rod A and rod B. you must toss into the water exactly one of each type of rod, every ten minutes, or the experiment overheats and you have a meltdown. the experiment will run for 100 minutes (so you have 10 of each type of rod), after which the uranium will be depleted and things are safe again.
the problem is that just as you started the experiment, your stupid lab assistant dropped the rods and they all got mixed up on the floor. and unfortunately, they all look alike, smell alike, weigh the same, taste the same and are pretty much indistinguishable! you have 10 minutes before the experiment gets going and you have to put in the first pair of rods to prevent a meltdown... and you have to put in exactly two of each rod every 10 minutes after that... put too few and you die... put too many, and you'll run out later and die... put in only one kind and you die...
what do you do??
you are running a very dangerous nuclear experiment. you are trying out a new form of putty-like control rods that are supposed to be much cheaper and more effective, but they become ineffective after exactly ten minutes in water and must be replaced. you have two types of rods: rod A and rod B. you must toss into the water exactly one of each type of rod, every ten minutes, or the experiment overheats and you have a meltdown. the experiment will run for 100 minutes (so you have 10 of each type of rod), after which the uranium will be depleted and things are safe again.
the problem is that just as you started the experiment, your stupid lab assistant dropped the rods and they all got mixed up on the floor. and unfortunately, they all look alike, smell alike, weigh the same, taste the same and are pretty much indistinguishable! you have 10 minutes before the experiment gets going and you have to put in the first pair of rods to prevent a meltdown... and you have to put in exactly two of each rod every 10 minutes after that... put too few and you die... put too many, and you'll run out later and die... put in only one kind and you die...
what do you do??
jimbob200521
Diamond Member
- Apr 15, 2005
- 4,108
- 29
- 91
Take all of the "putty like" rods, mix them together. Assuming that they can be mixed. Then seperate them out into 9 equal parts. Continue throwing 1 in every 10 minutes.
this is a paradox and such barber can't exist because you're implying the following two contradicting things:
1. the barber can't cut his own hair, or he'd be cutting the hair of some1 in the village who cuts his own hair
2. but then, if he doesn't cut his own hair... your statement that "the barber cuts the hair of EVERYBODY that doesn't cut his own hair" is violated.
x = child's current age
y = mom's current age
y = x + 21
y + 6 = 5 * (x + 6) --> y = 5x + 24
5x + 24 = x + 21
4x = -3
x = -3/4
no such child exists.
very close - if you mix it extremely well that should work.
the slightly more elegant solution i had in mind was that you'd lay all 20 rods out on a table and cut (very precisely) each rod into 10 pieces. so you have 20 piles of 10 pieces each. every 10 minutes, take 1 piece from each of the 20 piles - so you have 20 pieces total - and toss it in.
edited for clarity... yeesh my typing is bad
edit 2: forgot to mention that the original problem was formulated differently:
you are stranded on a desert island and everyday, you need to take two pills to live: pill A and pill B. you have ten of each pill and you know a rescue party will come by after ten days. the problem is that you mixed your pills up and they all look alike, smell alike, taste alike, etc...
although this is less "contrived" than the nuclear example... i find the solution (cutting each pill into 10 equal pieces) totally unrealistic for some1 on a desert island... so, i did my best to make it more reasonable
fair enough, after rereading it, you are right. although the typical formulation does imply that he ONLY cuts the hair of those who don't cut their own, so it is usually a paradox. i suppose we could also be picky and say that the problem implies that there are actually two barbers. "... in this village there is a barber. And a very special barber". which would also allow the answer of the very special barber being the one to cut the other barber's hair
right, i forgot to answer the actual question... of course, in reality, we all know the father is actually at work and it's the milkman that's... working hard
it will but you have to realize what corners they're talking about. one plank crosses from one side of the outer corner to the other side. the other plank extends from one corner of the island toward the corner of the outer square and lands in the middle of the other plank.
No, I get the concept, but I still don't think it'll work. The moat is 10 yards(30 feet) and the planks are only 9 feet.
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