Number of ways to break a stick
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Number of ways of breaking a stick of length $ngeq1$ into $n$ pieces of unit length (at each step break one of the pieces with length $geq1$ into two pieces of integer lengths) is what?
I couldn’t figure out how to approach this question, can someone help me out?
combinatorics permutations combinations
asked Jan 17 at 19:05
user601297user601297
40019
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add a comment |
0
$begingroup$
Number of ways of breaking a stick of length $ngeq1$ into $n$ pieces of unit length (at each step break one of the pieces with length $geq1$ into two pieces of integer lengths) is what?
I couldn’t figure out how to approach this question, can someone help me out?
combinatorics permutations combinations
asked Jan 17 at 19:05
user601297user601297
40019
$endgroup$
1
$begingroup$
The points to break are clear, now we only need to take an order on them to get a breaking strategy...
$endgroup$
– dan_fulea
Jan 17 at 19:08
$begingroup$
Can you please elaborate
$endgroup$
– user601297
Jan 17 at 19:09
$begingroup$
Ok no need i get it now, answer should be (n-1)!, right ?
$endgroup$
– user601297
Jan 17 at 19:11
1
$begingroup$
Take a stick of length 5, so [0-1-2-3-4-5], now the breaking points are 1,2,3,4, take a permutation say 1234 $to$ 4132, then break first in 4, then in 1, ... So we count permutations finally...
$endgroup$
– dan_fulea
Jan 17 at 19:12
$begingroup$
Excellent, well done!
$endgroup$
– dan_fulea
Jan 17 at 19:12
add a comment |
0
0
0
$begingroup$
Number of ways of breaking a stick of length $ngeq1$ into $n$ pieces of unit length (at each step break one of the pieces with length $geq1$ into two pieces of integer lengths) is what?
I couldn’t figure out how to approach this question, can someone help me out?
combinatorics permutations combinations
asked Jan 17 at 19:05
user601297user601297
40019
$endgroup$
Number of ways of breaking a stick of length $ngeq1$ into $n$ pieces of unit length (at each step break one of the pieces with length $geq1$ into two pieces of integer lengths) is what?
I couldn’t figure out how to approach this question, can someone help me out?
combinatorics permutations combinations
combinatorics permutations combinations
asked Jan 17 at 19:05
user601297user601297
40019
asked Jan 17 at 19:05
user601297user601297
40019
asked Jan 17 at 19:05
user601297user601297
40019
asked Jan 17 at 19:05
user601297user601297
40019
asked Jan 17 at 19:05
user601297user601297
40019
40019
1
$begingroup$
The points to break are clear, now we only need to take an order on them to get a breaking strategy...
$endgroup$
– dan_fulea
Jan 17 at 19:08
$begingroup$
Can you please elaborate
$endgroup$
– user601297
Jan 17 at 19:09
$begingroup$
Ok no need i get it now, answer should be (n-1)!, right ?
$endgroup$
– user601297
Jan 17 at 19:11
1
$begingroup$
Take a stick of length 5, so [0-1-2-3-4-5], now the breaking points are 1,2,3,4, take a permutation say 1234 $to$ 4132, then break first in 4, then in 1, ... So we count permutations finally...
$endgroup$
– dan_fulea
Jan 17 at 19:12
$begingroup$
Excellent, well done!
$endgroup$
– dan_fulea
Jan 17 at 19:12
add a comment |
1
$begingroup$
The points to break are clear, now we only need to take an order on them to get a breaking strategy...
$endgroup$
– dan_fulea
Jan 17 at 19:08
$begingroup$
Can you please elaborate
$endgroup$
– user601297
Jan 17 at 19:09
$begingroup$
Ok no need i get it now, answer should be (n-1)!, right ?
$endgroup$
– user601297
Jan 17 at 19:11
1
$begingroup$
Take a stick of length 5, so [0-1-2-3-4-5], now the breaking points are 1,2,3,4, take a permutation say 1234 $to$ 4132, then break first in 4, then in 1, ... So we count permutations finally...
$endgroup$
– dan_fulea
Jan 17 at 19:12
$begingroup$
Excellent, well done!
$endgroup$
– dan_fulea
Jan 17 at 19:12
1
1
$begingroup$
The points to break are clear, now we only need to take an order on them to get a breaking strategy...
$endgroup$
– dan_fulea
Jan 17 at 19:08
$begingroup$
The points to break are clear, now we only need to take an order on them to get a breaking strategy...
$endgroup$
– dan_fulea
Jan 17 at 19:08
$begingroup$
Can you please elaborate
$endgroup$
– user601297
Jan 17 at 19:09
$begingroup$
Can you please elaborate
$endgroup$
– user601297
Jan 17 at 19:09
$begingroup$
Ok no need i get it now, answer should be (n-1)!, right ?
$endgroup$
– user601297
Jan 17 at 19:11
$begingroup$
Ok no need i get it now, answer should be (n-1)!, right ?
$endgroup$
– user601297
Jan 17 at 19:11
1
1
$begingroup$
Take a stick of length 5, so [0-1-2-3-4-5], now the breaking points are 1,2,3,4, take a permutation say 1234 $to$ 4132, then break first in 4, then in 1, ... So we count permutations finally...
$endgroup$
– dan_fulea
Jan 17 at 19:12
$begingroup$
Take a stick of length 5, so [0-1-2-3-4-5], now the breaking points are 1,2,3,4, take a permutation say 1234 $to$ 4132, then break first in 4, then in 1, ... So we count permutations finally...
$endgroup$
– dan_fulea
Jan 17 at 19:12
$begingroup$
Excellent, well done!
$endgroup$
– dan_fulea
Jan 17 at 19:12
$begingroup$
Excellent, well done!
$endgroup$
– dan_fulea
Jan 17 at 19:12
add a comment |
0
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1
$begingroup$
The points to break are clear, now we only need to take an order on them to get a breaking strategy...
$endgroup$
– dan_fulea
Jan 17 at 19:08
$begingroup$
Can you please elaborate
$endgroup$
– user601297
Jan 17 at 19:09
$begingroup$
Ok no need i get it now, answer should be (n-1)!, right ?
$endgroup$
– user601297
Jan 17 at 19:11
1
$begingroup$
Take a stick of length 5, so [0-1-2-3-4-5], now the breaking points are 1,2,3,4, take a permutation say 1234 $to$ 4132, then break first in 4, then in 1, ... So we count permutations finally...
$endgroup$
– dan_fulea
Jan 17 at 19:12
$begingroup$
Excellent, well done!
$endgroup$
– dan_fulea
Jan 17 at 19:12