1. For every positive integer n, the function h(n) is defined to be the product of alll the even integers from 2 to n, inclusive. If p is the smallest prim factor of h(100)+1, the p is ? 答案：more than 40
Suppose you have ABCDE sitting on a table. Then you have "another" BCDEA sitting on the table. If you walk around the table, you 'will find these two arrangements are the same! So is CDEAB, DEABC, and EABCD. That's why you need to devide what you get from a linear arrangement by 5 in the circular case.
Linear arrangements of ABCDE, BCDEA, CDEAB, DEABC, and EABCD are all unique arrangements, in part because the head and toe positions are occupied by different letters.
Circular arrangements of ABCDE, BCDEA, CDEAB, DEABC, and EABCD are the same setup because the chairs around the table are not labeled (只要旁边的人相同都只算一种). In all five instances, A is always between B and E, B is always between A can C , etc.
The difference between circular and linear setups is the at the former has no head or tail positions.
Because you assume the first one chose is the "head" and the last one you chose is the "tail" around the table. In reality, neither head nor tail exist around the table.
To assign 5 people around a table, you do the following: 1) Pick one person and let it sits on one seat on the table. 2) Pick another from the remaining 4 and let it sit to the left of the first one: 4 possibilities 3) Pick another from the remaining 3; left; of the 2nd: 3 possibilities 4) Pick another, 2; left; 3rd: 2 possibilities.
No. The first one we picked does not count. Think about in this way: Let's suppose the first one is A. no matter how the arrangements are, each person, including A, has to have a seat somewhere around the table. Then we just start with A EVERY SINGLE TIME. So A's position is fixed. What is changing is the other 4 people's seats relative to A.
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发表于 2011-4-2 12:38:39
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