# Monthly Archives: मार्च 2009

## >Brain Teasers

>1.The Rope Bridge

Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time.

Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

2.The Oldest Plays the Piano

Two MIT math grads bump into each other while shopping at Fry’s. They haven’t seen each other in over 20 years.

First grad to the second: “How have you been?”

Second: “Great! I got married and I have three daughters now.”

First: “Really? How old are they?”

Second: “Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there…”

First: “Right, ok… Oh wait… Hmm, I still don’t know.”

Second: “Oh sorry, the oldest one just started to play the piano.”

First: “Wonderful! My oldest is the same age!”

How old was the first grad’s daughter?

## >Brain Teasers -Solutions

>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.