No one of us knew the age of Lisa, our math teacher,
and the six guesses were as follows:
34,47,48,53,30 and 40.
When confronted with this list , Lisa joyfully said:
I will not disclose my age explicitly, but I let you know
that all of you erred.
Your estimates were off by: 2,6,11,12,8,5.
Well, it took some reasoning to get her true age.
What was it?
This was an easy task, since one could quickly find the overlap in possible ages for a couple of guessers and then expand, and would not need to explore all possible combinations. No programming needed.
This arrived at 42 as the teacher's true age.
34 + 8
47 - 5
48 - 6
53 - 11
30 + 12
40 + 2
Compare the two extreme guesses, i.e. 30 and 53: only 41 or 42 are shared. Then note that the next younger (34) can not reach 41, so 42 must be the common age, as is confirmed by applying that to the other three guesses.
Edited on October 14, 2010, 3:14 pm