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More than one way to skin a cat (Posted on 2010-03-24) Difficulty: 2 of 5
You start with a zero and try to reach exactly 100 in 4 stages, each stage consisting of either increasing or decreasing your current number by a factorial n!( number like 1,2,6,24,120,720 etc) .
How many sequences exist to accomplish this task?

See The Solution Submitted by Ady TZIDON    
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Solution Let me count the ways -- computer solution | Comment 4 of 6 |
   5   dim H(4)
  10   gosub *AddOn
  20   end
1010   *AddOn
1020   local I,Ch
1030   inc Lvl
1040   for I=1 to 40
1045      Ch=!(I)
1050      Tot=Tot+Ch:H(Lvl)=Ch
1060      if Lvl=4 and Tot=100 then Ways=Ways+1:print Ways,H(1);H(2);H(3);H(4)
1070      if Lvl<4 then gosub *AddOn
1080      Tot=Tot-2*Ch:H(Lvl)=-Ch
1090      if Lvl=4 and Tot=100 then Ways=Ways+1:print Ways,H(1);H(2);H(3);H(4)
1100      if Lvl<4 then gosub *AddOn
1110      Tot=Tot+Ch
1200   next
1210   dec Lvl
1250   return
finds
1       2  2 -24  120
2       2  2  120 -24
3       2 -24  2  120
4       2 -24  120  2
5       2  120  2 -24
6       2  120 -24  2
7      -2  6 -24  120
8      -2  6  120 -24
9      -2 -24  6  120
10     -2 -24  120  6
11     -2  120  6 -24
12     -2  120 -24  6
13      6 -2 -24  120
14      6 -2  120 -24
15      6 -24 -2  120
16      6 -24  120 -2
17      6  120 -2 -24
18      6  120 -24 -2
19     -24  2  2  120
20     -24  2  120  2
21     -24 -2  6  120
22     -24 -2  120  6
23     -24  6 -2  120
24     -24  6  120 -2
25     -24  120  2  2
26     -24  120 -2  6
27     -24  120  6 -2
28      120  2  2 -24
29      120  2 -24  2
30      120 -2  6 -24
31      120 -2 -24  6
32      120  6 -2 -24
33      120  6 -24 -2
34      120 -24  2  2
35      120 -24 -2  6
36      120 -24  6 -2

That's 36 ways, but really only two fundamentally different sets of numbers: -24, 2, 2 and 120; and -24, -2, 6 and 120, with 12 permutations of the former and 24 of the latter.


  Posted by Charlie on 2010-03-24 12:49:05
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