Bill ran into his neighbor from across the hall and asked her how old her children were. She replied, “Let’s see if you can figure it out. The product of their ages is 72 and the sum of their ages is the same as my apartment number.” Bill thought for a while and then replied, “You haven’t given me enough information.” His neighbor replied, “Oh I forgot to tell you that my youngest child has asthma.” Now bill knew the ages of each child. How old is each?
Bill is better than me. I don't even know how many children she has. She could have twins who are one year old.
To solve this puzzle, we need to find the ages of the neighbor's children. We know that the product of their ages is 72 and the sum of their ages is the same as the neighbor's apartment number.
Let's start by finding the possible combinations of numbers whose product is 72. To determine all possible combinations, we can list all the factors since 72 can be factored as follows:
1 x 72 = 72
2 x 36 = 72
3 x 24 = 72
4 x 18 = 72
6 x 12 = 72
8 x 9 = 72
Now let's consider the sum of their ages, which will be the same as the neighbor's apartment number. Since the neighbor initially thought that this information was not enough, there must be multiple combinations with the same sum. To find the possible sums, we can list all the combinations:
1 + 72 = 73
2 + 36 = 38
3 + 24 = 27
4 + 18 = 22
6 + 12 = 18
8 + 9 = 17
Now, let's take into account the fact that the neighbor's youngest child has asthma. This implies that there is an age that appears only once among the possible combinations of sums.
Looking at the list of sums, we can see that the number 17 appears only once. Therefore, we can conclude that the ages of the neighbor's children are 8 and 9, with the youngest child being 8 years old and the oldest child being 9 years old.