Blog of Code

To brighten up the gala dinner of the IOI’98 we have a set of N coloured lamps numbered from
1 to N. The lamps are connected to four buttons:
button 1 — when this button is pressed, all the lamps change their state: those that are ON are turned OFF and those that are OFF are turned ON.
button 2 — changes the state of all the odd numbered lamps.
button 3 — changes the state of all the even numbered lamps.
button 4 — changes the state of the lamps whose number is of the form 3K+1 (with K >= 0), i.e., 1,4,7,…
There is a counter C which records the total number of button presses.
When the party starts, all the lamps are ON and the counter C is set to zero.

Some people believe that there are three cycles in a person’s life that start the day he or she is born. These three cycles are the physical, emotional, and intellectual cycles, and they have periods of lengths 23, 28, and 33 days, respectively. There is one peak in each period of a cycle. At the peak of a cycle, a person performs at his or her best in the corresponding field (physical, emotional or mental). For example, if it is the mental curve, thought processes will be sharper and concentration will be easier.
Since the three cycles have different periods, the peaks of the three cycles generally occur at different times. We would like to determine when a triple peak occurs (the peaks of all three cycles occur in the same day) for any person. For each cycle, you will be given the number of days from the beginning of the current year at which one of its peaks (not necessarily the first) occurs. You will also be given a date expressed as the number of days from the beginning of the current year. You task is to determine the number of days from the given date to the next triple peak. The given date is not counted. For example, if the given date is 10 and the next triple peak occurs on day 12, the answer is 2, not 3. If a triple peak occurs on the given date, you should give the number of days to the next occurrence of a triple peak.

There are nine clocks in a 3*3 array (figure 1). The goal is to return all the dials to 12 o’clock with as few moves as possible. There are nine different allowed ways to turn the dials on the clocks. Each such way is called a move. Select for each move a number 1 to 9. That number will turn the dials 90′ (degrees) clockwise on those clocks which are affected according to figure 2 below.

Consider the following 5 picture frames placed on an 9 x 8 array.
Now place them on top of one another starting with 1 at the bottom and ending up with 5 on top. If any part of a frame covers another it hides that part of the frame below.
Viewing the stack of 5 frames we see the following.

n 皇后问题研究的是如何将 n 个皇后放置在 n×n 的棋盘上，并且使皇后彼此之间不能相互攻击。