I was a little disappointed that so few people are interested in mathematics (or in this case, logic). My next problem will be pure mathematics, just in case it’s logic that people don’t like, but I’m still not optimistic.
Before reading the answers, be sure you’ve read the original post: Logic Problems #1.
The key here is to notice that a 1-digit number costs 20 cents, 2 digits cost 40 cents, and 3 digits cost 60 cents, so pricing seems to be dependent on the number of digits. This would make sense if the guy was buying a house number.
Since the product of the ages of the three kids is 72, write out all possible lists of the three ages: [1,1,72], [1,2,36], [1,3,24], [1,4,18], [2,2,18], [1,6,12], [2,3,12], [1,8,9], [2,4,9], [3,4,6], [2,6,6], and [3,3,8].
If you add each of the three ages, the sum is different in every case except for [2,6,6] and [3,3,8], where they add to 14. When the first mathematician says that the information is insufficient to find the ages, the only way that could have happen was if the three age for two different lists are the same (which means that the second mathematician had to have taken $14 from his billfold).
By knowing that there is an oldest child, their ages must have been 3, 3, and 8.
Both of the first two problems came from a Scam School video. If you like problems of this type or also want to learn simple magic tricks, check out that site.
First, I’ll copy the list of possible dates that Hannah gave to Fred and George.
If the day that Hannah gave to George is the 18th or 19th, he would immediately know the date of Hannah’s birthday. Since Fred is sure that George doesn’t know her birthday, the month that Hannah gave him must have been July or August. Fred’s first remark immediately lets George in on this fact.
If the day given to George is the 14th, he couldn’t know her birthday, but since his remark indicates that he does, the day has to be the 15th, 16th, or 17th, which would immediately give him the month.
Knowing that George now knows her birthday, Fred also realizes that the day can only be the 15th, 16th, or 17th. However, for Fred to know her birthday, the month he was given must have only one possible date remaining in it, and that would be July.
Hannah’s birthday is July16.
The first I heard of this problem was probably on either Fox Radio or one of the Christian radio stations I occasionally listen to. There I found out that this is a problem on a Common Core test for fifth graders and that actual mathematicians were unable to solve. Fortunately, I’m not an actual mathematician. And now you know why the television show Are You Smarter Than a Fifth Grader? is so challenging.
Obviously, neither of those assertions remotely has anything to do with reality. It actually comes from the Singapore and Asian Schools Math Olympiad for 14-year olds to sort out the top 40% of their students. It might give you some idea why America lags so far behind so many other nations in STEM programs. If you want more information, it was originally called Cheryl’s birthday problem.
Rest easy in the knowledge that you may still be smarter than a fifth grader.