Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Please help me with the following question
Replies: 78   Last Post: Mar 25, 2013 1:38 AM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Joe Niederberger Posts: 4,657 Registered: 10/12/08
Re: Please help me with the following question
Posted: Mar 8, 2013 3:12 PM
 Plain Text Reply

>In those several hours, what was your strategy?

I hope my spaces hold - else this will just look a mess:

A. ABCD = EFGH (A thru H OK)
A.1 IJ = KA (L light or heavy)
A.1.a L < A (L is light)
A.1.b L > A (L is heavy)
A.2 IJ < KA (I or J light) or (K heavy)
A.2.a I = J (K is heavy)
A.2.b I < J (I is light)
A.2.c I > J (J is light)
A.3 IJ > KA (I or J heavy) or (K light)
(exercize)

B. ABCD < EFGH (I thru K OK)
B.1 ABE = CFI (D light) or (G or H heavy)
B.1.a G = H (D is light)
B.1.b G > H (G is heavy)
B.1.c G < H (H is heavy)
B.2 ABE < CFI (A or B light) or (F heavy)
B.2.a A = B (F is heavy)
B.2.b A > B (B is light)
B.2.c A < B (A is light)
...
etc. etc. etc.

- ----------------------------------
To call it a "strategy" is a bit grandiose, but I know the key points. Somehow I got the idea (after giving up on others) to weigh ABCD versus EFGH first. Then I completed the A branch (above where the ABCD~EFGH weighing balances). The logical assertions (in the parenthesis) from the complete "A" branch clued me in on what to shoot for. I needed the further inspiration at some point to come up with a weighing like B.1, where some coins switch sides, some drop out, and some come in from the sidelines (maybe I was thinking sports.) But it leads to a logical assertion of the same form as was already dealt with in the "A" branch.

- ----------------------------------------
Now, I should've said "not all that hard in retrospect." At the time, I'm sure it was the hardest of my father's puzzles that I had solved. There are no doubt others I never solved and have forgotten, but others (age 6? 7?) that I didn't solve and asked for the answer (The farmer, chicken, fox and boat.)
- ---------------------------------------------

All that being said, I'm still impressed with the
so-called "communications channel" approach referenced earlier. I've seen the same essential idea explained differently. I've even used it myself at a much older age (grad school). No matter. I get the distinct feeling that kind of approach could crush problems that my 10-year-old poking around "strategy" sketched above could never get near. Though its beyond me at the moment to explain why.

Cheers,
Joe N

Date Subject Author
2/24/13 hydraflap
2/24/13 Richard Strausz
2/25/13 James Elander
2/27/13 Wayne Bishop
3/1/13 GS Chandy
3/1/13 GS Chandy
3/5/13 johnykeets
3/7/13 Joe Niederberger
3/7/13 Robert Hansen
3/7/13 Joe Niederberger
3/7/13 Joe Niederberger
3/7/13 Robert Hansen
3/7/13 Joe Niederberger
3/7/13 Joe Niederberger
3/7/13 Robert Hansen
3/7/13 Robert Hansen
3/7/13 GS Chandy
3/7/13 Robert Hansen
3/7/13 GS Chandy
3/7/13 GS Chandy
3/7/13 Robert Hansen
3/7/13 GS Chandy
3/7/13 GS Chandy
3/7/13 Joe Niederberger
3/7/13 Joe Niederberger
3/8/13 GS Chandy
3/8/13 GS Chandy
3/8/13 GS Chandy
3/8/13 GS Chandy
3/8/13 GS Chandy
3/8/13 Robert Hansen
3/8/13 Joe Niederberger
3/8/13 Robert Hansen
3/8/13 Joe Niederberger
3/8/13 Robert Hansen
3/8/13 Joe Niederberger
3/8/13 Robert Hansen
3/8/13 Joe Niederberger
3/9/13 Robert Hansen
3/8/13 Joe Niederberger
3/8/13 Joe Niederberger
3/9/13 GS Chandy
3/9/13 Robert Hansen
3/8/13 GS Chandy
3/9/13 GS Chandy
3/8/13 GS Chandy
3/9/13 Joe Niederberger
3/9/13 Robert Hansen
3/10/13 Robert Hansen
3/9/13 GS Chandy
3/10/13 GS Chandy
3/10/13 GS Chandy
3/10/13 Joe Niederberger
3/10/13 Robert Hansen
3/10/13 GS Chandy
3/11/13 Robert Hansen
3/11/13 Joe Niederberger
3/11/13 Robert Hansen
3/11/13 Robert Hansen
3/11/13 Joe Niederberger
3/11/13 Robert Hansen
3/11/13 Joe Niederberger
3/11/13 Robert Hansen
3/11/13 Robert Hansen
3/12/13 Joe Niederberger
3/12/13 GS Chandy
3/13/13 GS Chandy
3/13/13 Robert Hansen
3/13/13 Joe Niederberger
3/13/13 Robert Hansen
3/13/13 Joe Niederberger
3/14/13 Robert Hansen
3/14/13 Robert Hansen
3/15/13 GS Chandy
3/14/13 Joe Niederberger
3/14/13 Robert Hansen
3/14/13 Joe Niederberger
3/15/13 GS Chandy
3/25/13 VALERY

© The Math Forum at NCTM 1994-2018. All Rights Reserved.