Problem 1 Multiples of 3 or 5

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.

Problem 2 Even Fibonacci numbers

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …
By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

Problem 3 Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?

Problem 4 Largest palindrome product

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers.

Problem 5 Smallest multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Problem 6 Sum square difference

The sum of the squares of the first ten natural numbers is：

$$
\large 1^2+2^2+3^2+\cdots+10^2=385
$$

The square of the sum of the first ten natural numbers is：

$$
\large (1+2+3+\cdots+10)^2=55^2=3025
$$

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is：

$$
\large 3025 - 385 = 2640
$$

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Problem 7 10001st prime

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10 001st prime number?

Problem 8 Largest product in a series

The four adjacent digits in the 1000-digit number that have the greatest product are $9×9×8×9=5832$.

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?

Problem 9 Special Pythagorean triplet

A Pythagorean triplet is a set of three natural numbers, $a < b < c$, for which,

$$
\large a^2+b^2=c^2
$$

For example,

$$
\large 3^2+4^2=9+16=25=5^2
$$

There exists exactly one Pythagorean triplet for which $a + b + c = 1000$.
Find the product $abc$.

实验内容

根据数据库 db_student 中的 tb_student 表、tb_score、tb_course，完成下列查询语句

表结构

表结构如下：

• tb_student(sno,sn,dept,sex,birthday,polity)
• tb_score(sno,cno,score)
• tb_cource(cno,cn,ct)
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