International Mathematics Olympiad for Primary School - 2013
4th Grade Math Test in Violympic Math contest for Elementary Students - Vong 19
Hướng dẫn Giải Đề thi Violympic Giải toán trên mạng Lớp 4 - Vòng 19 - năm học 2012 - 2013
International Mathematics Olympiad for Primary School - 2013 - Answer the following 6 questions, and show your detailed solution in the space provided after each question. Each question is worth 10 points.
Time limit: 60 minutes.
In a mathematical competition consisting of 25 problems, 8 marks are given for each correct response, 0 marks for each incorrect response and each no response is awarded 3 marks. Tom scored 121 marks in this competition. What is the smallest number of incorrect responses he could have?
How many numbers less than 1000 have the product of their digits equal to 63?
The integers 1, 2, 3, .. , 2005 are written on the board. What is the smallest number of these integers that can be wiped off so that the product of the remaining integers ends in 8?
How many numbers less than 4000 can be formed with the digits 2, 3, 4, 5 and 6 if no digit is used more than once in a number?
In a soccer tournament eight teams play each other once, with two points awarded for a win, one point for a draw and zero for a loss. How many points must a team score to that it is in the top three (i.e. has more points than at least five other teams)?
Two players take it in turns to choose from 25 numbered counters, each labeled with a different odd number from 1 to 49. When one player chooses a counter labeled X, the next player must choose the counter whose label is the greatest odd factor 0f 99..X. No matter what the first counter be taken, what is the least number of counters will remain when the game ends?
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