想想孩子们！
Think Of The Children!
题目详情
一个众所周知的逻辑问题是这样的：人口普查员（安迪）和 男人（鲍勃）正在交谈：
安迪：您有多少个 18 岁或以下的孩子？ 鲍勃：3 安迪：他们几岁了？ 鲍勃：嗯，他们的年龄乘积是 72，他们的年龄之和与我的地址相同。 安迪：我还是不能确定他们的年龄。 鲍勃：哦，我应该提一下，我最大的孩子比我的其他两个孩子都大。 安迪：好的，现在我知道你的孩子多大了。
除了 72，Bob 可以说出的下一个最大数字是多少，这样剩下的对话就可以以同样的方式进行？
A well-known logic problem goes something like this: A census-taker (Andy) and a man (Bob) are having a conversation:
Andy: How many children 18 or younger do you have? Bob: 3 Andy: How old are they? Bob: Well, the product of their ages is 72, and the sum of their ages is the same as my address. Andy: I still can’t determine their ages. Bob: Oh, I should mention that my oldest child is older than either of my other 2 children. Andy: Ok, now I know how old your children are.
Instead of 72, what is the next largest number that Bob could have said, such that the rest of the conversation could have proceeded the same way?
解析
为了让谈话能够像现在这样进行，这个时代的产物 鲍勃的孩子需要能够以两种不同的方式进行考虑，其中之一 最大的 2 个因子彼此相同，并且具有相同的 因素的总和。例如，对于 72，安迪会不确定鲍勃是否 即使知道他的地址是 14，孩子们的年龄也为 (8,3,3) 或 (6,6,2)，直到 他的最后一个问题得到了解答。
满足这些限制的下一个最大数字是288。部分提交者 将“下一个最大”解释为小于 72 的最大数，而不是 大于 72 的最小数字。由于这有点模糊，我们接受 36 作为 也正确。
最常见的错误答案之一是 225，人们认为鲍勃的 孩子们可能是 (25,3,3) 或 (15,15,1)。然而，25岁对于成为一个人来说太老了 孩子！
恭喜所有正确的响应者，尤其是 Alice Scarpa，这 本月随机选出的 Jane Street T 恤优胜者！
Original Explanation
In order for the conversation to proceed as it did, the product of the ages of Bob’s children needs to be able to be factored in 2 different ways, one of which has the largest 2 factors being the same as each other, and which have the same sum of factors. For example, with 72, Andy would have been unsure whether Bob’s children were aged (8,3,3) or (6,6,2) even knowing his address was 14, until having his final question answered.
The next largest number that satisfies these constraints is 288. Some submitters interpreted “next largest” to mean the largest number smaller than 72, not the smallest number larger than 72. Since this was a bit vague, we accepted 36 as correct as well.
One of the most popular incorrect answers was 225, with the thought that Bob’s children could have been (25,3,3) or (15,15,1). However, 25 is too old to be a child!
Congratulations to all of the correct responders, especially Alice Scarpa, this month’s randomly-chosen winner of a Jane Street t-shirt!