Monday, 21 September 2015

Rust remover

When you are trying to solve a problem, sometimes your worldview causes you to unintentionally import prejudices and assumptions that block you from the solution. 

To illustrate, here is an updated version of a puzzle that completely baffled me when I was a kid. In this day and age it won’t fool very many people, and in fact, many people would not see a problem at all.
A father and his son were in a car accident and were taken by ambulance to the hospital. The father was injured, but not seriously, and he was sent to the waiting room. However, the son needed surgery. After he was prepped for the operation, the surgeon came in, but said “I can't operate on him — he's my son!” How is this possible?
When I was young, I subconsciously pictured a doctor as being a man, and this prevented me from seeing the solution, namely that the surgeon was the child’s mother. (Of course, nowadays we recognize that there is a second solution: the surgeon was the son’s other father.)

While I was still teaching I often began one particular course with a small collection of puzzles like this. I used to call them Rust Removers because the students’ thinking always seemed a bit rusty after returning from their summer or Christmas break.

Here’s a dozen puzzles that were carefully posed to entice you into following your preconceptions or somehow cause you to make unwarranted assumptions. You may be able to solve most of them quickly, but very few of my students were able to solve all of them in one sitting. 

If you are absolutely desperate for an answer, a pdf file of the solutions is available here.

1. One night John was reading an exciting book when a power failure threw the room into complete darkness. Nevertheless, he continued reading without a pause. He was not using a laptop, tablet, or e-reader, so how could he do that?
2. I live in a modern high-rise apartment. A lady friend who regularly visits me always gets off the elevator five floors below mine and takes the stairs to my floor. Why?
3. Last night I turned off the light in my bedroom and managed to get into bed before the room was dark. My bed is 3 metres from the light switch. How did I do it?
4. A woman walked up to a counter and handed a book to the cashier. He looked at it and said “Ten dollars.” She paid the man and walked out without the book.  He saw her leave without it but did not call her back.  How come?
5. A man is found shot to death in the front seat of his car. A gun lies out of his reach in the back seat.  All the windows are closed and the doors are locked; there are no bullet holes anywhere in the car. How could this have happened?
6. An escaped prisoner was running along a forest road when he saw a cop car heading towards him. He sprinted into the woods, but before doing this he ran ten metres directly towards the approaching car. Why?
7. A woman had two sons who were born on the same hour of the same day of the same year. But they were not twins, and they were not adopted. How could this be so?
8. Jim Johnson lives in a four story apartment building. He is plant supervisor at an auto factory that is within walking distance of his apartment. Every morning at 0800 h, he walks down a flight of stairs, and when he arrives at his destination he settles back with a cup of Tim Hortons coffee that he purchased along the way and begins to read the newspaper. Halfway through the news his eyelids close and he falls asleep for several hours. Nevertheless, at the end of the month he looks forward to a nice pay raise. How does he get away with this?
9. Take 3 empty paper coffee cups, and put eleven coins in them so that each cup holds an odd number of coins. All the coins must be used. Once you have solved this, put 10 coins in the same cups so that again each cup holds an odd number of coins and all coins are used. (Remember, zero is an even number.) 

The following puzzle is now found throughout the web. I first saw it about 20 years ago. 
10. There is a light in a storage room on the second floor of a building. On the ground floor are three light switches, exactly one of which controls the storage room light, which is a standard incandescent 100 watt bulb. By turning some or all of the switches on or off, it is possible to determine which switch controls the light by making one trip to the storage room. How can this be done?
Outside the storage room, there is no way to determine whether the light is on or off, and disassembling the light switches will not reveal which one controls the light. You are not allowed to be helped by anyone.
11. Two grade six classes were going on a field trip to a museum. They were being transported by two buses each of which had 34 seats.  It so happened that there were 30 boys and 34 girls, and so they put all the boys on one bus and the girls on the other bus. The buses had to stop for a few minutes, and during that time 10 boys snuck onto the girls' bus. But the girls' bus driver noticed that there were too many on the bus, so he sent 10 children (boys and girls) back to the boys' bus. After this was done, were there more boys on the girls' bus than girls on the boys' bus? Or vice versa?

Another older puzzle that has also found its way onto the web:
12. Four people are being pursued by a menacing beast. It is nighttime, and they need to cross a bridge to reach safety. It is pitch black, and only two can cross at once. They need to carry a lamp to light their way. 
Mr. One takes a minimum of 1 minute to cross. Mr Two takes 2 minutes, Mr. Five takes 5 minutes, and Mr. Ten takes 10 minutes. 
If two cross together, the couple is only as fast as the slowest person. For example, if Mr. Ten and Mr. One cross the bridge together, it will take them 10 minutes. A fast person can't carry a slower person to save time. The person or couple crossing the bridge needs the lamp for the entire crossing, and the lamp must be carried back and forth across the bridge (no throwing, etc.). 
 If they don't all get completely across in strictly less than 19 minutes, who ever is on the bridge or left behind will be eaten by the beast. Is it possible for all of them to get across?

These puzzles are not mine. Some of them came from Martin Gardner’s book “aha! Insight!”  The book has a lot more than just these puzzles, and it can be read in selected short chunks. 

If you like short puzzles that challenge students to overcome fixations in their thinking, you should visit the WODB site. There you will find a collection of puzzles inspired by Christopher Danielson and curated by Mary Bourassa. Each puzzle presents four different things which are such that every three of them have at least one thing in common that is not shared by the fourth one. (WODB = Which One Doesn’t Belong.) 

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