[PDF] Top 20 2015 ITMO 個人賽試題參考解法

... 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。 ... See full document

... 10. What is the minimum number of fourth powers of integers, not necessarily distinct, such that their sum is 2015? 【Submitted by BURGAS】 【Solution】 Since 7 4 = 2401 2015 > , we can only use the fourth ... See full document

... 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] ... See full document

... 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] ... See full document

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

... 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] ... See full document

... 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] ... See full document

... 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] ... See full document

... Proper reasoning for the rest of the countries based on restrictions of already fixed colors up to 10 pts (here partial credits will be given based on the progress). Finding the corr[r] ... See full document

... 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] ... See full document

... 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] ... See full document

... 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] ... See full document

... Conclude that at least one of them must be greater than or equal to 2017 2015 , 20 marks. 3. There are 2016 unit cubes, each of which can be painted black or white. How many values of n is it possible to construct ... See full document

... Since A starts in an odd-numbered place and trades places an odd number of times, he must finish in an even-numbered position.. Since B starts in an even-numbered place and trades pla[r] ... See full document

... 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。 ... See full document

... Republication, systematic copying, or multiple reproduction of any part of this material is permitted only under license from the Chiuchang Mathematics Foundation. Requests for such p[r] ... See full document

... 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。 ... See full document

... 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。 ... See full document

... 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。 ... See full document

... 高中學生參加，本人當時帶領學生參加此競 賽，回來後，為了增進學生對於數學競賽的 興趣，針對個人賽的部分進行解法研討，發 現當時每兩個題目只能做 10 分鐘，和之後研 討後的解法有多處不同，思考方式也更加嚴 密 ， 也 發 現 一 個 問 題 有 時 不 會 ... See full document