Tuesday Teaser #11: Ripple Road 2
Oh crate Cod! This puzzle kicked my hiney, left it red and shiny. The Ripple Effect will take longer than the Country Road, my previous erratum notwithstanding.
The average size of a region is just slightly higher than for the previous puzzle, and the geometric mean is actually smaller, so I guess my added difficulty came from the increased grid area. (Okay, that and I composed the puzzle when I should have been asleep.) As for the unused numbers... well, let's say I think I answered all meanderlawn's questions.
On another note, this month's Math Magic has a bunch of questions, all of them worthy of attention. But I'd like to draw your attention to Problem 1, which defines something called a "multiplicative partition" for some integers. Read up; I'll wait.
Okay, so obviously a 1 in the partition results in a factor of 2 in the number of subsets with the right product. The integer 1 is treated specially because one of those subsets is the empty set (with empty product of 1). So my question is, if we throw out 1, does any odd integer have a multiplicative partition?
EDIT: Whoop! I found one already. But I think I'll sit on it for a few days, see if someone else gets one.
The average size of a region is just slightly higher than for the previous puzzle, and the geometric mean is actually smaller, so I guess my added difficulty came from the increased grid area. (Okay, that and I composed the puzzle when I should have been asleep.) As for the unused numbers... well, let's say I think I answered all meanderlawn's questions.
On another note, this month's Math Magic has a bunch of questions, all of them worthy of attention. But I'd like to draw your attention to Problem 1, which defines something called a "multiplicative partition" for some integers. Read up; I'll wait.
Okay, so obviously a 1 in the partition results in a factor of 2 in the number of subsets with the right product. The integer 1 is treated specially because one of those subsets is the empty set (with empty product of 1). So my question is, if we throw out 1, does any odd integer have a multiplicative partition?
EDIT: Whoop! I found one already. But I think I'll sit on it for a few days, see if someone else gets one.