On this week's list of the top 40 pop songs, last week's #35 is no longer on the list and a new song has appeared in the #32 position.
Positions 1, 23, 29, 31 and 37 have remained the same.
Each other song on last week's list has moved by an amount that is a factor, greater than 1, of last weeks position itself (including the possibility that the movement is in fact the same as last week's position).
If 18 of the 34 that moved moved up, and 16 moved down, what are the new positions of the songs listed by their position last week?
Apparently the postings are now accepted. I explained my solution method: to create a 40x40 grid to track the allowable movements. After allowing for the five which did not move (four couldn't anyway, by the rules), and setting aside 35 since the original song on that row was no longer ranked, I noted all possible new positions using the factors rule. I then iterated on this grid to reduce the options, and note when a single new position was locked in. This reduced the undecideds to about 10, and further logic deduced the undecideds to two (the new positions 12 and 18 could be held by either order of the original positions 09 and 15.
At this point I turned to the counts of "up" and "down". I assumed that with a list of this sort, "moving up" would mean going to a lower row number, and "moving down" to a higher row number -- but this would not work. I assigned 18 to row 9, and 12 to row 15, but this gave me 17 higher and 17 lower; and the alternate assignment of 12 to row 9, and 18 to row 15, gave me 16 higher and 18 lower. To make sense of the 16 and 18 counts, I then assumed that by "moving higher" you meant moving to numerically higher row. That would give the count 18 higher and 16 lower. My final list had the following pairings (original position first, new position second):
01:01 02:04 03:06 04:02 05:10 06:03 07:14 08:16
09:12 10:05 11:22 12:15 13:26 14:07 15:18 16:08
17:34 18:09 19:38 20:25 21:28 22:11 23:23 24:27
25:20 26:13 27:24 28:21 29:29 30:33 31:31 32:40
33:30 34:17 35n/a 36:39 37:37 38:19 39:36 40:35
An interesting puzzle, Charlie! I'll look at previous comments after I've posted.
Pocket full of wry
