CSE 21 HW 2

（1）（a）至少可以除以多少个三位数的正整数
6或7？
（b）[3000]中有多少个整数= {1,2,3，…。 。 。 ，2999、3000}不能被2、3或7整除吗？
（c）我们可以用多少种方式列出数字{1、1、2、2、3、4、5}，所以没有

（2）在每种情况下，都要编写一个递归关系，包括基本案例，

（a）令C（n）为n×n网格中1×1像元的数量。写一个
C（n）的重复发生。
（b）一堆摩托车和汽车要在一条街道上平行停放。的

C代表摩托车，C代表汽车，则这四种安排

（c）令B（n）为长度n的二进制字符串的数目，其中没有三个

（d）任何二进制字符串都可以分成相同的连续块

•长度为2的0s
•长度为3的1s
•长度为1的0的游程
•长度为1的1s
•长度为5的0s
Let B(n) be the number of length n binary strings where each run of
1s has even length. Find a recurrence for B(n).
(e) Let S(n) be the number of subsets of {1, 2, . . . , n} having the following
property: no two elements in the subset are consecutive integers. The
empty set with no elements should be included in your count. Write
a recurrence for S(n).
(f) A ternary string is like a binary string except it uses three symbols, 0,
1, and 2. For example, 12210021 is a ternary string of length 8. Let
T(n) be the number of ternary strings of length n with the property
that there is never a 2 appearing anywhere after a 0. For example,
12120110 has this property but 10120012 does not. Write a recurrence
for T(n).
Note: For parts (g) and (h) of this problem, to “tile a rectangle” is to
cover it with tiles so that no tiles overlap, no tiles are hanging off the
edge of the rectangle, and every space on the rectangle is covered by
some tile.

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