滑鐵盧大學數學競賽雖然今年取消了8月31號之前的所有競賽，但是學習不可以停滯不前。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
-----------------------------我是答案分割線------------------------------
1. 6
2.約等於0.443
3. 7
4. 39
5.C
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