tag:blogger.com,1999:blog-15628310.post4383315227660926591..comments2024-02-11T22:40:20.959-05:00Comments on Question of the day: A Farmer and His StonesAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-15628310.post-80590474001751871502008-09-24T07:16:00.000-04:002008-09-24T07:16:00.000-04:00As usual for these types of problems, there's a ma...As usual for these types of problems, there's a mathematical principle that guides the question.<BR/><BR/>But I have no idea what it is! ;-)<BR/><BR/>But you're right, Abe. The four stones are 1, 3, 9 and 27.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-44809436428183911882008-09-23T21:27:00.000-04:002008-09-23T21:27:00.000-04:00Well, they have to add up to 40, and you have to b...Well, they have to add up to 40, and you have to be able to build all the numbers from 1 to 40 with combinations of the 4 (adding -- putting more stones opposite the grain -- and subtracting -- adding the stones to the grain side of the scale). You're going to need various degrees of resolution, so it seems like you'll need a 1-pounder, then increasing weights.<BR/><BR/>If you guess that the first one is 1, then it seems reasonable that the second could be 3, which is the highest number you could use to make 2 (3-1). You can then make 3 and 4 easily. To make 5, you the highest number you can use is a 9 (9-3-1). You can make 6-13 with these. The highest number you can use to make 14 is 27 (27-9-3-1). You can make numbers 14-40 with these four stones: 1, 3, 9, and 27 pounds.<BR/><BR/>I can't put my finger on the significance of the fact that the stone weights are in powers of 3. Any thoughts?Abehttps://www.blogger.com/profile/04424868492071587450noreply@blogger.com