加拿大滑鐵盧數學競賽真題分享及答案！

Category: 數學國際競賽 Date: 2022年3月15日下午3:59

加拿大數學教賽體系在中國較為知名的，是滑鐵盧大學University of Waterloo舉辦的一系列以數學家為名的數學學術活動，從7年級到12年級各有對應的比賽。所以我們今天準備一些考試真題，快來做做看！

1.The digits from 1 to 9 are written in order so that the digit n is written n times. This forms the block of digits 1223334444 · · · 999999999. The block is written 100 times. What is the 1953rd digit written? (2018 Gauss 7)

2.In the diagram, two larger circles with radius 1 have centres P and Q. Also, the smaller circle has diameter PQ. The region inside the two larger circles and outside the smaller circle is shaded. The area of the shaded region is closest to (2018 Pascal 9)

3.The number of ways that 135 can be expressed as the sum of at leastt two consecutive positive integers is?

4.In a magic triangle, each of the six whole numbers 10-15 is placed in one of the circles so that the sum, S, of the three numbers on each side of the triangle is the same. The largest possible value for S is

5.Two different prime numbers between $4$ and $18$ are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?

A)? 22

B) 60

C)119

D) 94

E)231

答案：

1. 6

2.約等于0.443

3. 7

4. 39

5.C

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