Aunts and uncles
- Did I tell you about my aunts and uncles?
- No, you did not.
- Well, here goes. I have three of each. Three aunts married to three uncles.
- So, what is the problem?
- Does there have to be a problem?
- When I talk to you there usually is.
- The problem is that in each pair there is a heavy person and a light person.
- That is to be expected.
- The strange thing is that all the heavy persons weigh the same and all the light persons weigh the same.
- Remarkable!
- I have a scale balance with which I want to find the heavy one in each pair.
- How many weighings are enough?
- You said it!
March 24th, 2011 at 4:38 am
Refer to the couples as A, B, and C.
Arbitrarily pick a person from A and a person from B and compare their weights. If the scales show their weights differ, you’ve determined the heaver person in both A and B. So what remains is to compare the weights of the two folk in couple C and all has been revealed, in two weighings.
If the two people just compared from A and B have the same weight: keep one of them on the scale, to compare weights with a person arbitrarily picked from C. If they differ, the heavier and lighter folk in all the couples has been determined, with two weighings.
If that second comparison produced a tie, a third comparison is needed. Keep the same person from A on the scale, and compare with the other person from couple C. All is revealed, but this time 3 weighings were needed.
Certainly the interesting remaining question is the probability/odds of needing 2 versus needing 3 comparisons. By my reckoning, the probability is 3 in 4 that two weighings are sufficient. Then again, conditional probability has not ever been my strong suit.
March 25th, 2011 at 9:08 pm
March 26th, 2011 at 12:32 am
First there is a spoon, then there is no spoon…
What happened to swt? Admittedly that copy/paste was a mess, but it seems he/she had indeed bettered my solution.
March 26th, 2011 at 6:10 am
I think some of the “” were interpreted as html tags and the text inbetween was disappearing. I contacted Jan to correct/remove the posts and I reposted it as a picture.
March 26th, 2011 at 6:19 am
If the post by swt is not OK now I need to know in detail what is wrong. The current comment is text not an image.
March 26th, 2011 at 6:37 am
I sent you an e-mail with my thoughts on the problem
March 26th, 2011 at 7:02 am
Testing:
3<4
“3<4
“3<4″
<4
“<4
“<4″
I am not able to find out when the comments are not presented as they are typed. If you have this problem please post the comment as an image. If you can find out what the problem is I will add it as a warning. If you can also solve the problem you will be my hero.
March 26th, 2011 at 7:16 am
I’ll try my best and I let you know.
March 26th, 2011 at 7:46 am
You are welcome to post your test comments here. If they start with the word “Testing” I will delete them after a few hours.