鋸木棒難題

Assume every rod's lenght is 24 unit, then everybody can get 11units of rod.

every rod can give 2 x 11 units and 2 unit left.

Assume all rod cut to get 11 units out first, => Cut 11 times, and 11 people get the rod.

Now there is 11 rods with lenght 13 units long share for 13 people.
Let's take a look on the combination of 11

11=11+0, 10+1, 9+2, 8+3,7+4,6+5

The way to cut the 13 units rod:

11+2,9 + 4,7 + 6,5 + 8,3 + 10,1 + 12

After the 6 cuts, we have full fill 6 people's need
There is 5 rod's lenght 13 units and one 12 unit, for 7 people

11 + 1, 10 + 3, 8 + 5, 6 + 7, 4 + 9, 2 + 11.

After 6 more cuts, we have fullfill all 7 people's need.

total number of cuts = 11 + 6 + 6 =23 cuts.

2007-06-28 16:01:36 補充：
This is funny if the question is:There is 1 rod to divide for 24 peoples, then we have to cut 23 times.It seem that we can treat the question like this since the 11 rods can be treated as 1 rod only.

2007-06-29 10:27:44 補充：
If there is x rods and y people, the number of cuts to fullfill the needs is y-1 cuts.

2007-06-29 10:28:32 補充：
For x < y, and x is not a factor of y.

問題無話要分盡木棒,所以將六根木棒平分鋸斷,有十二根一樣長短的木棒,再鋸十二根,得二十四根。所以最少鋸12+6=18次,仲有五根中飽私囊^^

當每一枝長度為1米, 每人應得11/24米

每一枝要鋸兩次, 就等於11/24米 + 11/24米 + 2/24米
總共11枝, 暫時已鋸22次, 得22枝11/24, 及11枝2/24米
最後將其中一枝2/24, 鋸一次變成兩枝1/24, 就可得(2/24) x 5 + 1/24 = 11/24

完成, 共23 次