Urgent Help to solve another 3 maths problems

静雯 · 发表于 10-4-2012 17:06:15|来自：新加坡

Sorry, trouble everyone again.

Q1. A goat in a horizontal ground is tied to one end of 14 m long rope. The other end of the rope is attanched to a ring which is free to slide along a fixed 20 m long horizontal rail. Find the maximum possible area that the goat can graze.
Ignore the dimension of the ring and take pi to be 22/7.

The provided answer is 1204 square m, but my answer is 1176. How can I get 1204 or the answer is wrong?

静雯 · 发表于 10-4-2012 17:08:53|来自：新加坡

Q2. A theme part isssues entrance tickets bearing 5-digit serial numbers from 00000 to 99999. If any adjacent numbers in the serial numbers differ by 5 (for example 12493), customers holding such a ticket could use the ticket to reddem a free drink. Find the number of tickets that have serial numbers with this property.

静雯 · 发表于 10-4-2012 17:13:15|来自：新加坡

Q3.
P, Q, R, S and T are equally spaced on a straight rod. P----Q----R----S----T
If the rod is frist rotated 180 degree about T, then 180 degree about S and finally 180 degree about P, which point's position remains unchanged?

I don't understand why the provided answer is R. Isn't the answer wrong again?

jjrchome · 发表于 10-4-2012 23:23:05|来自：新加坡

本帖最后由 jjrchome 于 11-4-2012 00:00 编辑

Q1.
Taking account of the distance between "goat's mouth" and the knot (say 22cm), you will get 1204m2.

jjrchome · 发表于 10-4-2012 23:32:52|来自：新加坡

静雯发表于 10-4-2012 17:13
Q3.
P, Q, R, S and T are equally spaced on a straight rod. P----Q----R----S----T
If the rod is ...

Q3.

P----Q----R----S----T

T----S----R----Q----P

P----Q----R----S----T

T----S----R----Q----P

jjrchome · 发表于 10-4-2012 23:43:16|来自：新加坡

本帖最后由 jjrchome 于 10-4-2012 23:49 编辑

静雯发表于 10-4-2012 17:08
Q2. A theme part isssues entrance tickets bearing 5-digit serial numbers from 00000 to 99999. If any ...

这个是2011年Asia Pacific Mathematical Olympiad for Primary Schools第一轮竞赛的其中一道试题啊。

抄来的答案：

先求相邻2个不等于5的。
首位可取10个，第2、3、4、5位只能取9个，共10*9*9*9*9。
所以相差5的数有 100000-10*9*9*9*9=34390个

jjrchome · 发表于 10-4-2012 23:51:09|来自：新加坡

静雯发表于 10-4-2012 17:13
Q3.
P, Q, R, S and T are equally spaced on a straight rod. P----Q----R----S----T
If the rod is ...

中国的初一数学竞赛中也有一道类似的题：

jjrchome · 发表于 10-4-2012 23:53:47|来自：新加坡

本帖最后由 jjrchome 于 10-4-2012 23:54 编辑

顺便把Asia Pacific Mathematical Olympiad for Primary Schools 2011 1st round的试题给贴出来：

http://www.hexagon.edu.vn/download/110424_apmops2011.pdf