2014 Otago Problem Solving Competition 题目和解答

maylan

最近Year6的儿子参加了Otago problem solving competition ，据网页介绍这个考试要连续考五次，从四月份后的每个月考一次，每次有5个问题，然后以总成绩来排名。这种数学考试应是史上最长的考试了，真的要耐心等侯才知胜负。

据儿子说，Year6和Year7是同一张试卷，我看网页的排名也只有Year7以上的排名，难道Year6的学生们全军覆没还是网页没有公布Year6的排名？自1991年开考以来，只有Year9以上的试题，好象是近几年才开放到Year6-8。排名榜上的学生绝大部分是汉语拼音的名字，中国学生的数学成绩真是所向披靡呀！


感觉上大家比较重视澳洲的ICAS的考试，不少帖子里都讨论澳洲的统考，暨南大学新西兰实验学校等辅导中心还以ICAS的考试成绩做为教学评估。但是这本土的Otago大学为主的数学竞赛却很少人提起，希望了解这考试的家长和老师给些更详细的资料，网页里的内容很有限。做为家长需要买参考书给孩子题海练习吗？


http://www.maths.otago.ac.nz/pc/

http://www.maths.otago.ac.nz/jmc/JMChome.php

在发帖咨询时得到了热心网友的建议和解释，在其他参赛学生的回忆下，还原了Otago数学竞赛2014的题目及部分答案，Maths-NZ、Cindyppz（马大姐）帮助解答了竞赛难题。

maths_nz

maylan 发表于 2014-12-12 07:46
A:   8    3     2
     4           6
     1    7     5

很好，答案是1，5。

maths_nz

maylan 发表于 2014-12-12 08:53
答案是20。

19+1，17+3，13+7

1 is not prime number, try again.

maths_nz

maylan 发表于 2014-12-12 07:55
答案是100。

只有更改百位数的数字才能让5位数的前后顺序一致，所以100是两位数之间最小的差。

How about 20002 and 19991?

maylan

maths_nz 发表于 2014-12-4 07:53
Q7: there are six different prime numbers, a,b,c,d,e,f, all less than 20, such that a+b, c+d and e+f ...

答案是20。

19+1，17+3，13+7

不确定是不是这样解题，感觉是不是太简单了。

孩子圣诞前活动特别多，有时间再研究Q20，在稿纸演算了几遍不得要领暂时放弃。

maylan

maths_nz 发表于 2014-12-4 07:50
Q8: 16261 is a palindromic number as it reads the same forwards and backwards. Of all the possible p ...

答案是100。

只有更改百位数的数字才能让5位数的前后顺序一致，所以100是两位数之间最小的差。

maylan

maths_nz 发表于 2014-12-4 07:45
Q18: Each of the numbers 1,2,3,4,5,6,7,8 can be place into a circle so that the sum of the three num ...

A:   8    3     2
     4           6
     1    7     5


B:  5    7     1
     2           8
     6    3     4

maylan

maths_nz 发表于 2014-12-4 08:07
好像4号房子送了4次？

重新改正了答案：

Mon---1，2，5
Tue---1，4，7
Wed---2，4，5
Thu---1，2，7
Fri-----4，5，7

3号房子和6号房子没送。

maths_nz

maylan 发表于 2014-12-3 22:27
Monday-------1,2,5
Tuesday------1,4,7
Wednesday--2,4,5

好像4号房子送了4次？

maths_nz

涛声依旧 发表于 2014-12-3 18:53
19 boys。

是不是19个男孩太多了，不是16个？

maths_nz

maylan 发表于 2014-12-3 22:34
这道题不懂做，还是老师你来解答吧。

能不能把其他的题目贴出来，谢谢老师。

Q16: 速度实际上就是时间和距离的关系，一小时（60分钟）走四公里也就是一公里需要15分钟，同样一小时跑六公里也相当于一公里需要10分钟；也就是说一公里的路程跑和走差了5分钟，而实际上那段距离差了7分钟，所以路程就是7/5=1.4公里。

很多题目带有图，不会弄，只好上些没图的了。

maths_nz

Q7: there are six different prime numbers, a,b,c,d,e,f, all less than 20, such that a+b, c+d and e+f all have the same value. What is that value?

maths_nz

Q8: 16261 is a palindromic number as it reads the same forwards and backwards. Of all the possible palindromic 5-digit numbers, what is the smallest difference between any two?

maths_nz

Q18: Each of the numbers 1,2,3,4,5,6,7,8 can be place into a circle so that the sum of the three numbers along any of the four sides of the figure is 13. There are two solutions. What two numbers occur in the corners of both solutions?

O O O
O.    O
O O O

maths_nz

Q20: Replace each of the nine different letters in this sum by one of the digits 1,2,3,4,5,6,7,8,9 to make the arithmetic correct. When this is done, what is the number "HIDE"?
      A D I B H C A
+.  G D A B I E C
-------------------------
      C E H G F E G

maylan

maths_nz 发表于 2014-11-29 07:53
Q16: Simon can walk at 4 kilometres per hour and run at 6 kilometres per hour. He finds he can save  ...

这道题不懂做，还是老师你来解答吧。

能不能把其他的题目贴出来，谢谢老师。

maylan

maths_nz 发表于 2014-11-29 08:16
Q4: In a set of five numbers, three of the numbers have an average of 15 and the other two have an a ...

（3*15+2*10）/  5

=65/5

=13

这道题是几个题目最为简单的了。

maylan

maths_nz 发表于 2014-11-29 08:06
Q19: There are seven houses in Chanllenge Street, number 1 to 7. One week the postman noticed that e ...

Monday-------1,2,5
Tuesday------1,4,7
Wednesday--2,4,5
Thursday----1,4,5
Friday---------4,5,7

House 3 and House 6 had not get any mail.

涛声依旧

maths_nz 发表于 2014-11-29 06:57
Q9: at a party there were 25 students. Maria danced with eight boys, Irene with nine, Anna with ten  ...

19 boys。


这题比较简单，照次序排列就可以找出男孩的数量了。

涛声依旧

maths_nz 发表于 2014-11-29 06:50
写几道今年final的题，没机会做的的小朋友如果感兴趣的话可以一试。
Q15: Harry fills a bottle with wine. ...

            

  1.   1/3  +  2/3  =   1

  2.   1/9 +  2/9   =   1/3
      
       2/9  +  4/9   =   2/3

3.    1/3+2/9   :    4/9

      =  5/9  ：     4/9

      =   5：4




         



1/3-1/9：

maylan

pl_pingli 发表于 2014-4-14 17:33
你说的这个考试，是针对7-8年级的，少量六年级的学生可以参加，但好像是不能参加最后的总决赛final challen ...

没错，六年级的小朋友就是陪考，即使初赛总分达到决赛要求，也不给机会参加决赛的考试。

maylan

maths_nz 发表于 2014-11-6 14:39
选拔题及答案：
http://www.mathsolympiad.org.nz/wp-content/uploads/2014/08/2014_NZMOC.pdf
http://www. ...

谢谢老师的资料推荐，好全面。

maths_nz

Q4: In a set of five numbers, three of the numbers have an average of 15 and the other two have an average of 10. What is the average of all five numbers?

maths_nz

Q19: There are seven houses in Chanllenge Street, number 1 to 7. One week the postman noticed that each day he delivered mail to exactly three houses, and the sums of the three house numbers were: Monday 8, Tuesday 12, Wednesday 11, Thursday 10, Friday 16. He also realized that over the week he had left mail at five of the houses three times each. At which houses had he not left any mail?

maths_nz

Q9: at a party there were 25 students. Maria danced with eight boys, Irene with nine, Anna with ten and so on for all the girls up to the last girl Casey who danced with all the boys. How many boys were at the party?

maths_nz

Q16: Simon can walk at 4 kilometres per hour and run at 6 kilometres per hour. He finds he can save 7 minutes by running instead of walking from his house to the dairy. What is the distance in kilometres from his house to the dairy?

maths_nz

写几道今年final的题，没机会做的的小朋友如果感兴趣的话可以一试。
Q15: Harry fills a bottle with wine. He then removes 1/3 of the contents and fills up the bottle with water. He mixes the liquids and then removes 1/3 of the contents and again fills up the bottle with water. What is the ratio of water to wine in the bottle?

maths_nz

选拔题及答案：
http://www.mathsolympiad.org.nz/ ... 4/08/2014_NZMOC.pdf
http://www.mathsolympiad.org.nz/ ... 2014-Solutions1.pdf

maths_nz

The invitation to 2015 NZMOC January Camp has been distributed to 24-28 students. If you're one of them, congratulations! If you are not, don't be too discouraged, because bear in mind that 24-28 are chosen among 100 genius mathematicians who attempted the Camp Selection Problems; you should be proud with the fact that you have participated in the competition aimed at students with great mathematical potential.
For 2015 Campers, the Stage 1 of the journey to the IMO has been completed. The rest of the post will be about Stage 2: squad selection...
Visit the website to read the full post
http://www.nzmosa.org/blog/5-11-2014-selected-for-camp-what-now

maths_nz

四个太阳 发表于 2014-9-1 14:47
我家闺女数学基础一般，problem solving不错。
老师建议试试参加为奥数准备的camp。
看看奥数的题，直接 ...

如果过去没有专门的奥林匹克训练，孩子对奥数感兴趣，建议从NZMOSA网页开始，这个是由新西兰学生数学奥林匹克学会拥有的网页，其实是几个往年新西兰代表队的学生义务创办的，目的是为了帮助高水平数学学生更进一步，每个月他们都会推出三套初级，中级，高级试题给有兴趣同学，不妨就从这里开始。
http://www.nzmosa.org/monthly-competitions/