最近有人喜欢做数学题，我儿子在袁老师那儿学的题

[ChineseOne]

The Chocolate Allergy Revelation

A travelling salesperson shows up at the apartment of a math teacher to peddle her wares. During the course of her spiel, the salesperson discovers that the teacher has three children and inquires as to their ages.
The teacher answers, "The sum of my children's ages is 13."

The salesperson immediately declares, "That's not enough information to deduce your kids' ages!"

The teacher continues, "Well, the product of their ages is the same as my apartment number."

After taking a quick check of the apartment number, the salesperson thinks for a minute but then sighs, "That's STILL not enough information for me to figure it out."

So the teacher says, "Oh, I forgot to mention, my eldest child is allergic to chocolate."

At which point the salesperson exclaims, "Aha, now I know all their ages!"

What are the ages of the children?

（注：袁老师是加拿大中华儿童教育学会的国际象棋和奥林匹克数学特训班的老师和教练，他的学生（嘻嘻，有我的儿子在内）在加拿大学生国际象棋中都是Top Level，网址：www.cccei.org）

 

[吾言]

刚做完中文应用题，英文的又来了。看着晕。

 

[辟邪]

没看明白:blowzy:

 

[ChineseOne]

嘻嘻,中国来的才俊门，傻了吧！

请博士来解啊。这可是给小学3年级学生做的。

 

[游民]

今天赌钱时又丢了色子，只丢了两下：2和2，所以最大的小孩试9岁，还有一对双胞胎

 

[ChineseOne]

最初由 无业游民 发布
今天赌钱时又丢了色子，只丢了两下：2和2，所以最大的小孩试9岁，还有一对双胞胎

 

[游民]

岁数只能是整数，和是13，积是门牌数。看了门牌还不知道岁数，说明积不唯一。只有 9，2，2和6，6，1符合条件。而后面一种情况就有有两个大孩子。巧克力是个烟幕弹

再来一个！

 

[Emy]

How do you know the product is 36?

 

[游民]

I didn't know the product. What I knew is the guy couldn't figure out the ages even he knew the product.

 

[tutu007]

最初由 Emy 发布
How do you know the product is 36?

杀鸡焉用牛刀，就这样的题还需要博士？

枚举三个小孩的年龄，从大排到小，可能的方式有以下几种：
11 1 1 -> 11
10 2 1 -> 20
9 3 1 -> 27
9 2 2 -> 36
8 4 1 -> 32
8 3 2 -> 48
7 5 1 -> 35
7 4 2 -> 42
7 3 3 -> 63
6 6 1 -> 36
6 5 2 -> 60
6 4 3 -> 72
5 5 3 -> 75
5 4 4 -> 80
积重复的值只有 36，如果门牌号是其他的值，则第二个条件就会有结果；
第三个条件告诉我们年龄最大的孩子只有一个；
因此结果是 9 2 2。

 

[ChineseOne]

最初由 无业游民 发布
岁数只能是整数，和是13，积是门牌数。看了门牌还不知道岁数，说明积不唯一。只有 9，2，2和6，6，1符合条件。而后面一种情况就有有两个大孩子。巧克力是个烟幕弹

再来一个！

看样子，才俊们都成了无业游民了，可悲啊！加拿大树多，鸟多，问了我儿子，他说最近袁老师有一题:
Birds in Trees

A teacher asked a student the following question:

Our courtyard has more than one tree, and each tree contains more than one bird. Each tree has the same number of birds in it as the next tree, and there are between 200 and 300 birds in the courtyard. How many trees are in the courtyard?
The student was stumped. However, when the teacher told her how many birds were in the courtyard, she quickly solved the problem.

How many trees were in the courtyard?

袁老师就是用这些题目，训练学生下棋，最近渥太华市青少年国际象棋冠军赛，袁老师的两个女学生夺得了冠亚军。前五名中他的学生包办了4个。嘻嘻！我儿子的成绩也不坏。（不是做广告，实在是想让大家分亨www.cccei.org）

 

[CoHo]

17

 

[游民]

最初由 CoHo 发布
17

绝!
俺以后要卖了XBOX送小无业游民去袁老师那儿

袁老师,有更难的么?需要琢磨个两三天的?

 

[Kent以东首帅哥]

最初由 ChineseOne 发布


看样子，才俊们都成了无业游民了，可悲啊！加拿大树多，鸟多，问了我儿子，他说最近袁老师有一题:
Birds in Trees

A teacher asked a student the following question:

Our courtyard has more than one tree, and each tree contains more than one bird. Each tree has the same number of birds in it as the next tree, and there are between 200 and 300 birds in the courtyard. How many trees are in the courtyard?
The student was stumped. However, when the teacher told her how many birds were in the courtyard, she quickly solved the problem.

How many trees were in the courtyard?

袁老师就是用这些题目，训练学生下棋，最近渥太华市青少年国际象棋冠军赛，袁老师的两个女学生夺得了冠亚军。前五名中他的学生包办了4个。嘻嘻！我儿子的成绩也不坏。（不是做广告，实在是想让大家分亨www.cccei.org）

俺英文不好,什么叫"Each tree has the same number of birds in it as the next tree"?是说第一棵树上的鸟和第二棵上一样多,第二棵和第三棵一样多,最后一棵和第一棵一样多?

 

[淼]

其实抽象出来就是寻找一个200-300之间的合数（因为树和鸟必须大于1），它能被表示成两个因子的积并且只有唯一一种表示方式, 也就是某个数的平方。你也可以枚举，只有17x17满足条件。