>1.The Rope Bridge
To get everyone across in 17 minutes, we need get the two slowest people across together; otherwise we are wasting too much time. Once we get them across, how do we not make one of them walk back with the flashlight? Just have one of the faster people already there waiting to sprint the flashlight back across.
person A: 1 minute
person B: 2 minutes
person C: 5 minutes
person D:10 minutes
1. A & B cross. total time: 2 minutes.
C |==========================| A
D | | B
|==========================| flashlight
2. B comes back. total time: 4 minutes.
C |==========================| A
D | |
B |==========================|
flashlight
3. C & D cross. total time: 14 minutes.
B |==========================| A
| | C
|==========================| D
flashlight
4. A comes back. total time: 15 minutes.
A |==========================| C
B | | D
|==========================|
flashlight
5. A & B cross. total time: 17 minutes.
|==========================| A
| | B
|==========================| C D
flashlight
Another valid solution is to have A bring the flashlight back in step 2.
2.The Oldest Plays the Piano
The possible ages ( factors of 72 ) and their sums are shown below:
Ages: Sum of ages:
1 1 72 74
1 2 36 39
1 3 24 28
1 4 18 23
1 6 12 19
1 8 9 18
2 2 18 22
2 3 12 17
2 4 9 15
2 6 6 14
3 3 8 14
3 4 6 13
We can deduce from the man’s confusion over the building number that this wasn’t enough information to solve the problem. The chart shows the sum 14 twice for two different age possibilities, which would explain how knowing the building number alone would not have given him the answer. The clue that the “oldest one” started to play the piano rules out “2 6 6” as an answer, because there is no “oldest”. Since the first grad was certain with the piano clue, the first grad’s oldest daughter is 8.
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