... 8. If ABCD and KLFC are two squares so that B, K and L are collinear. Points M and P are on AC, points N and Q are on BD so that MNPQ is also a square, as shown in the figure below. If MN = BK and area of quadrilateral ...

5

... On the second day, the youngest brother divided all the remaining candies into five equal parts with one remaining candy, and then this youngest brother took two parts.. On the third d[r] ...

8

... For problems involving more than one answer, points are given only when ALL answers are correct.. Each question is worth 5 points.[r] ...

7

... 允許**學**生**個****人**、非營利性的圖書館或公立**學**校合理使用 本基金會網站所提供之各項**試****題**及其解答。可直接下載 而不須申請。 重版、系統地複製或大量重製這些資料的任何部分，必 須獲得財團法人臺北市九章數**學**教育基金會的授權許 可。 ...

7

... What is the minimum number of police squads so that every square not occupied by a police squad must share a side with a square occupied by a police squad. ANSWER: police squads.[r] ...

12

... In this case, there are 3 ways to choose the column to colour the 2 squares, and 2 ways to choose which one gets the other coloured square. Then there are 3 ways to choose which row th[r] ...

7

... The sum of all the numbers above the main diagonal (diagonal from the top-left cell to the bottom-right cell) is equal to three times the sum of all the numbers below the main diagonal[r] ...

6

... Form edges along the dotted lines to create shapes so that each circle is the symmetry center (each shape when rotated 180 degrees along the circle, the shape appears identical) of the[r] ...

12

... Deduced that the numbers on the diagonal should all be 11 and arrived with the correct answer, or correct answer only (without any explanation), 5 marks. In the figure below, ABCD is [r] ...

10

... Each correct figure, 10 marks. 10 marks bonus for all 3 correct figures. 6. There are three 3-digit numbers ABC , BCD and CDE , where each different letter represents a different digit, so that ABC + BCD + CDE = ...

11

... A computer randomly chooses three different points on the given grid below (all points have the equal chance of being chosen). Let p[r] ...

12

... What is the minimum number of weightings needed to find the fake marble and determine whether the fake marble is heavier or lighter than the real marble. Explain your answer.[r] ...

10

... 7. Anna tosses 2016 coins and Boris tosses **2017** coins. Whoever has more heads wins. If they have the same number of heads, then Anna wins. What is the probability of Anna winning? 8. In triangle ABC, AC = BC. D is ...

3

... At the end of the contest, you must hand in the envelope containing the question paper, your answer sheet and all scratch papers... Each weighs an integral numbers of kilograms?[r] ...

3

... If (1) occurs, then Anna wins, and if (2) occurs, then Boris wins, regardless of the outcome of Boris’ last toss.. If (3) occurs, then the winner will be decided by the outcome of Bori[r] ...

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... 10. ⼩德將他的蘋果顆數之⼀半給了⼩⾙，接著將剩下的蘋果顆數之⼀ 半給了⼩莎，最後他還剩下⼀顆蘋果。請問他原來有多少顆蘋果？ (A) 12 (B) 8 (C) 6 (D) 4 (E) 2 11-20 **題**，每**題** 4 分 11. 請問下列哪⼀**個**選項中的陰影部分⾯積最⼤？ ...

9

... In the 4 by 4 square shown, I am filling in the 16 small squares with the numbers 1, 2, 3 and 4 so that each row and each column has one of each of these numbers... I have a rectangular [r] ...

9

... The four lines from the top vertex divide the triangle into five narrow triangles with same area. The three lines parallel to the base divide the triangle into four horizontal strips[r] ...

4

... For problems involving more than one answer, points are given only when ALL answers are correct.. Each question is worth 5 points.[r] ...

7

... For problems involving more than one answer, points are given only when ALL answers are correct.. Each question is worth 5 points.[r] ...

6