Time Limit: 2000MS Memory Limit: 65536K Total Submissions: 10444 Accepted: 2089

###### Description

You are given three n × n matrices A, B and C. Does the equation A × B = C hold true?

Time Limit: 2000MS Memory Limit: 65536K Total Submissions: 10444 Accepted: 2089

You are given three n × n matrices A, B and C. Does the equation A × B = C hold true?

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 4753 Accepted: 2821

Given a string s of length n, a subsequence of it, is defined as another string s’ = su1su2…sum where 1 ≤ u1 < u2 < … < um ≤ n and si is the ith character of s. Your task is to write a program that, given two strings s1 and s2, checks whether either s2 or its reverse is a subsequence of s1 or not.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 2203 Accepted: 1630

The magician shuffles a small pack of cards, holds it face down and performs the following procedure:

The top card is moved to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades.

Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades.

Three cards are moved one at a time…

This goes on until the nth and last card turns out to be the n of Spades.

This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, 1 ≤ n ≤ 13.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 2414 Accepted: 1632

The D-pairs of a string of letters are the ordered pairs of letters that are distance D from each other. A string is D-unique if all of its D-pairs are different. A string is surprising if it is D-unique for every possible distance D.

Consider the string ZGBG. Its 0-pairs are ZG, GB, and BG. Since these three pairs are all different, ZGBG is 0-unique. Similarly, the 1-pairs of ZGBG are ZB and GG, and since these two pairs are different, ZGBG is 1-unique. Finally, the only 2-pair of ZGBG is ZG, so ZGBG is 2-unique. Thus ZGBG is surprising. (Note that the fact that ZG is both a 0-pair and a 2-pair of ZGBG is irrelevant, because 0 and 2 are different distances.)

Acknowledgement: This problem is inspired by the “Puzzling Adventures” column in the December 2003 issue of Scientific American.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 5675 Accepted: 3377

For any even number n greater than or equal to 4, there exists at least one pair of prime numbers p1 and p2 such that

n = p1 + p2

This conjecture has not been proved nor refused yet. No one is sure whether this conjecture actually holds. However, one can find such a pair of prime numbers, if any, for a given even number. The problem here is to write a program that reports the number of all the pairs of prime numbers satisfying the condition in the conjecture for a given even number.

A sequence of even numbers is given as input. There can be many such numbers. Corresponding to each number, the program should output the number of pairs mentioned above. Notice that we are interested in the number of essentially different pairs and therefore you should not count (p1, p2) and (p2, p1) separately as two different pairs.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 4491 Accepted: 2325

There is a sequence of n+2 elements a0, a1, …, an+1 (n <= 3000, -1000 <= ai <=1000). It is known that ai = (ai-1 + ai+1)/2 - ci for each i=1, 2, …, n.

You are given a0, an+1, c1, … , cn. Write a program which calculates a1.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 5969 Accepted: 3039

What do you do if you need to copy a 560x400mm image onto a standard sheet of US letter-size paper (which is about 216x280mm), while keeping the image as large as possible? You can rotate the image 90 degrees (so that it is in “landscape” mode), then reduce it to 50% of its original size so that it is 200x280mm. Then it will fit on the paper without overlapping any edges. Your job is to solve this problem in general.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 6719 Accepted: 4601

Businessmen, of course, can make much money. However, sometimes, they would lose money in trading. For example, Jame, a businessman, brought in some goods each cost him 40 yuan and he decided to sell at the price of 70 yuan. Then a customer came to buy one, gave Jame 100 yuan, and of course got back 30 yuan. You may said, “Jame earned 30 yuan.” But unfortunately, Jame found the 100 yuan from the customer was fake. What a poor man! In this case Jame lost 70 yuan (40 (the goods price) + 30 (the money paid back to the customer)).

Now your task is to calculate how much Jame would lose in this kind of trade. Of course in this case, sometimes Jame may still earn.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 6276 Accepted: 2424

Children are taught to add multi-digit numbers from right-to-left one digit at a time. Many find the “carry” operation - in which a 1 is carried from one digit position to be added to the next - to be a significant challenge. Your job is to count the number of carry operations for each of a set of addition problems so that educators may assess their difficulty.

Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 2872 Accepted: 1734

Now that you’re back to school for another term, you need to remember how to work the combination lock on your locker. A common design is that of the Master Brand, shown at right. The lock has a dial with 40 calibration marks numbered 0 to 39. A combination consists of 3 of these numbers; for example: 15-25-8. To open the lock, the following steps are taken:

```
turn the dial clockwise 2 full turns
stop at the first number of the combination
turn the dial counter-clockwise 1 full turn
continue turning counter-clockwise until the 2nd number is reached
turn the dial clockwise again until the 3rd number is reached
pull the shank and the lock will open.
```

Given the initial position of the dial and the combination for the lock, how many degrees is the dial rotated in total (clockwise plus counter-clockwise) in opening the lock?