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?

(In reply to Solution by Sing4TheDay)

Don't you have 17 of each?  Numbered, they come out

1  1 *
2  4
3  6
4  2 Up
5  10
6  3 Up
7  14
8  16
9  18
10  5 Up
11  22
12  15
13  26
14  7 Up
15  12 Up
16  8 Up
17  34
18  9 Up
19  38
20  25
21  28
22  11 Up
23  23 *
24  27
25  20 Up
26  13 Up
27  24 Up
28  21 Up
29  29 *
30  33
31  31 *
32  0  x
33  30 Up
34  17 Up
35  40
36  39
37  37 *
38  19 Up
39  36 Up
40  32 Up

The "Up"s number 17 as to the blanks (the *'s represent no change and the x doesn't count--only 34 count). So regardless of which column is considered the old position and which the new, and which way is up, there are 17 of each.

Posted by Charlie on 2009-01-29 18:08:59