Waterloo 2010 cayley last question

1: First of all, we need to simplify, because the dial is 10 numbers, and the remainder of 10 (expressed by %10) is 0, so we just need to put n n%10 (n=1,2,3...).1232, 1233, 1234) and %10 is the final answer.

2: To simplify again, since we only need the numbers on n n digits, then we can ignore the numbers on the other digits of the base n when calculating n n, as follows:

Two rows of 20 in a group, wait and talk about why)

In the end, there is 1234% left 20=14, i.e.

3: The most important thing is to find the law Let's take a look at the result of (1) and (2) for the remainder of 10.

1) As with (2), 20 is a cycle of 1 group, and 10 are added symmetrically in a row and then the remainder of 10 is 7 (coincidence?). ), a total of 123 rows, and the last 4 are left, which is the 4 numbers in front of the second row group, hahahaha.

I'll start by telling you why this is happening, and I'm excited myself.

1:1 n=1,2:2 2=4,2 12%10=(2 10*2 2)%10=(1024*4)%10=6,2 22%10=(2 10*2 12)%10=(1024*6)%10=4, that is, the cycle of 4 and 6, the adjacent sum is 0

3:3 3%10=7,3 13%10=(3 8*3 2*3 3)%10=1*9*7%10=3 (because 3 4%10=1), 3 23%10=(3 8*3 2*3 13)%10=1*9*3%10=7, that is, the cycle of 3,7, the adjacent addition is 0

4:4 4%10=6,4 14%10=(4 10*4 4)%10=(2 20*4 4)%10=(1024*1024*4 4)%10=6, that is, all 6

5：5^m%10=5

6：6^m%10=6

7: 7 7%10=3,7 17%10=(7 8*7 2*7 7)%10=(1*49*7 7)%10=7,7 27%10=(7 8*7 2*7 17)%10=(1*49*7 17)%10=3, that is, the cycle of 3 and 7, the adjacent additions are 0

8:8 8%10=6,8 18%10=(8 10*8 8)%10=(2 30*8 8)%10=(1024*1024*1024*6)%10=4, that is, the cycle of 6 and things, the adjacent sum is 0

9: 9 m (m is odd) %10 = 9 (because the mantissa multiplied by even 9s is 1).

Needless to say, 10:0.

So the final result is (7*123+1+6+3+6)%10=7

1^1≡1(mod10)

2^2≡4(mod10)

3^3≡7(mod10)

4^4≡6(mod10)

5^5≡5(mod10)

6^6≡6(mod10)

7^7≡3(mod10)

8^8≡6(mod10)

9^9≡9(mod10)

10^10≡0(mod10)

High digits do not affect.

After a round of cycling, 1 1 + 2 2 + ......10 10 7 (mod10) 1234 steps after moving steps 7 * 123 + 1 + 4 + 7 + 6 9 (mod10) dial indication 9

The city of Waterloo is a university city in eastern Canada, located in southern Ontario, 1 hour west of Toronto and an hour drive from Niagara Falls. Adjacent to another city, Kitchener, it is known as the K-W "Twin Cities".

The town of Waterloo is about twenty kilometers south of Brussels, the capital of Belgium. Like many other small towns in Europe, Waterloo is quaint and quiet, with little character, but its name is so resounding that even those who don't know much about it often say that someone who has lost a lawsuit or a game is bound to say that Waterloo has befallen so-and-so.

in Belgium. The town of Waterloo is about twenty kilometers south of Brussels, the capital of Belgium.

Mature students are adult students, most of whom graduated a long time ago and later went back to school after working for a while. If you are a new graduate, fill in no

Personally, I think (unofficial): the Battle of Waterloo changed the landscape of Europe at the time, Napoleon's Hundred Days was overthrown, Napoleon himself was exiled to St. Helena, and soon the July Dynasty was established and the French Revolution was over.

Prussia, on the other hand, became a military power in Europe, and the borders of the countries were redivided. And this battle also has a certain breakthrough in tactics.

There is upstairs in the course of the war, so I won't write about it.

See the encyclopedia for details. In short, the battle ultimately decided the fate of Napoleon and his empire, with far-reaching consequences for Europe.

Napoleon

In 1815, at Waterloo, Belgium, Napoleon led the French army to a fierce battle with the British and Prussian forces, and the French army suffered a crushing defeat. Subsequently, Napoleon ended his political career by abdicating. ”

What I want to say is that this drama is not about teenagers' jujube books - why is this Chinese translation name so weird, but I recommend watching this drama Very cute British students.

I don't know where the LSD answer came from, so it's too easy to come to Waterloo, right?

Different departments have different requirements, IELTS is the minimum requirement for general departments, and COOP is at least.

The tuition problem, a course in the freshman year is a little more than 2,000, and the more expensive it is, but it is also more than 2,000.

The annual tuition fee comes according to the number of courses you take and the number of semesters you take, just multiply it by yourself, and the messy miscellaneous fees for each semester are about 100, and some of them can be refunded.

Other expenses depend on how LZ has passed, living in school must be much more expensive, it is cheaper to go out and live by yourself, and it is cheaper to cook by yourself......I'm not going to dwell on it.

If you have less than three points in speaking, you can try to contact the school and explain it, just say that you don't play well in the exam, balabala should be avoided.

Even if I read ESL (usually called ELAS), it's good to be able to meet a lot of friends, and that's how I came ......

LZ just saw that I typed so many words in the middle of the night, and gave me a small 5 points ......

Hahaha

good luk ：）

Qualifications: a. 84% or above in 3-year high school average.

b, IELTS or TOEFL score of 88 or above.

Basic Tuition: Approximately $16,000 CAD per year on average.

Other expenses: Accommodation, board, transportation, etc.: approximately $10,000 per year.

I am an international student who graduated from Waterloo in 06 with a degree in Actuarial Science, I hope the following will be helpful to you.

1。Actuarial science has quite high requirements for mathematics. Calculus and linear algebra are secondary, and they rely primarily on statistical knowledge.

Seeing that your results in the college entrance examination are so good, you must have a good foundation. You don't need to be able to participate in competitions to learn actuarial science, so you don't have to worry about that.

2.I encourage you to apply for Coop, which takes a little longer, about 5-6 years. However, the work experience accumulated during the school years is very useful for finding a job after graduation.

Regular, depending on the individual's arrangement, most people finish it in 4 years.

3.Legal, do you mean the relevant commercial law? If yes, it's just an elective. Does medical stuff help actuarial science? Or maybe you're already thinking about doing health insurance.

There are quite a few requirements for computers. When I first studied, I had at least three courses in computer programming, which was not a shallow level for someone who had no idea about programming.

4.It's really tempting to see what you said about ivey. It's not funny, I don't know much about this aspect.

Choosing the right path for you is the best. Good luck in the end!

Since you are so good in the college entrance examination, and it is also a famous university in China, why do you have to go out, even if you go out, why is it waterloo ???Waterloo's computer science is nothing to say, actuarial science I don't know, the third problem: the courses in the university are both compulsory and optional

You have to dabble in almost everything.

Ivey is absolutely awesome business school, the domestic reputation is very high, so high that others only know Ivey and don't know the degree of Xi'an, waterloo you tell others that many people don't know, you can go to Ivey of course it, I hope you can apply for it

I don't know about the second question...

email:

She can help you explain it in detail.