Monday, July 22, 2019

Some Lateral/Math Problems

During my long teaching career I was teaching and tutoring math, physics, logic, and more, and also a Problem-Solving course to ITT-Technical students. For that course I used some of the problems from the list below. But before that, I used similar problems to stir a conversation about logic, creativity and problem-solving strategies with teachers taking my professional development workshops.

To become a successful physics teacher I have developed specific strategies for teaching student how to develop a solution to a problem: some of them are presented on this page.

Some of the lateral problems from my Problem Solving Course.

LtP1
This is the situation.
The General Electric decided to hire several more electricians, and you are the one of the applicants.
You already have successfully taken different tests, and now you are having the last one.
The hiring person leads you in the room, gives you this picture and says this.
“You can see three switches in the room #1: switch # 1, switch # 2 and switch # 3. They are absolutely identical, you never can find any difference between them, no matter what you would do to the switches.
There is the room #2 behind this door down to a corridor. There is a regular incandescent bulb in that room. I tell you that there is one and only one from these switches that turns that bulb on.
There is no window in that room, the walls are thick, the door is closed, and there is a second door at the end of the corridor that is closed, too, so, when you are in the room #1 you cannot see or hear anything happening in the room #2. But you can stay in the room #1 as long as you need playing with the switches and thinking. Then you can go to the room #2, but you will not be able to leave that room any more. I will be waiting for you in the room #2. When you come to me, you cannot go back, and must tell me what switch turns the bulb on, and you must prove it to me. Good luck!”
How can you solve this problem and get hired?

LtP2
In a dresser, there are five pairs of red socks and five pairs of black socks mixed up together. What is the minimum number of socks we need to take out the dresser without peeking to get a pair of the same color? What is the minimum number of socks we need to take out the dresser without peeking to get a pair of the red socks?

LtP3
A 1-gallon milk jug is being placed in the middle of a room. Can a man get into it?

LtP4
To buy a cake and a cup of tea you need 2 dollars and 25 cents. The cake costs 2 dollars more than the tea. How much do you need to buy just the tea?

LtP5
If we make all students of the class sit by two at a table, we got seven students without place to sit. But if we make the students of the class sit by three at a table, we got five free tables. How many students are in the class?

LtP 6
There are 111 players participating in the US Open tennis competition. Everybody who loses a game is dropped from the tournament. How many games totally will be played during the tournament?

LtP7
Mister Smith rents an apartment on the 35th floor of the Empire State Building. Every day in a morning when walking to his work he takes an elevator to get from his floor to the first floor. After the work on his way back to the apartment he uses the elevator from the first floor to the 30th, and the rest of the way he walks up. Why?

LtP8
You have two ropes. If you put them on fire at one end, the first one burns out in 30 minutes, but the second one in 60 minutes. How can you measure 45 minutes time interval having these ropes and a lighter?  Note: the ropes might be burning with different speeds, you know only the total time needed to get completely burned.

LtP9
You have two balls of same size and mass and color, but one has an cavity inside. How can you find which one has it?

LtP10
You have 12 identical coins, but you know that one is a fake (it might be a little heaver or lighter than the other). You have a two-plate balance. How can you find which coins is fake if you can make use the balance three only times?
Water is filling up an empty tank. Every hour the tank gets twice more water than it had an hour ago. It takes 10 hours to fill up the tank. How many hours is needed to fill a half of it?

LtP11
Two trench diggers dig 2 yards in 2 hours. How many trench diggers are needed to dig 12 yards in 6 hours?

LtP12
In a family, every daughter has the same number of sisters and brothers; but every son has twice more sisters than brothers. How many children are in the family?

LtP13
The length of Loch Ness Monster is equal to 20 yards and the half of its length. How long is Loch Ness Monster?

LtP14
One and a half hens lay down one and a half eggs in one and a half days. How many eggs will 2 hens lay in 3 days? How many eggs will 6 hens lay in 6 days?

LtP15
A family of a husband and a wife, a son, and a grandma needs to cross a river walking over a very old bridge during a pitch-dark night. The bridge can hold only two persons at the time. The family has only one flashlight, and no one can cross the bridge in the dark. The man can cross the bridge in 1 minute, his wife – in 2 minutes, the son in 5 minutes, and the grandma in 10 minutes. How can they cross the bridge in no more than 17 minutes?

LtP16
Two thirds of a male population are married to a female, and three fifth of the female population are married to a male (there are no other marriages in this old math problem). What portion of the populating is married?

LtP17
When a store received 1000 pounds of fresh cucumbers, each cucumber was 99 % made of water. The store could not sell a single one cucumber, and over time some water evaporated and the percentage of water in each cucumber fell to 98 %. How much do cucumbers weigh now?

LtP18
Huckleberry Finn spent 5 days to travel down the Mississippi river on a steam boat. Then on the same steam boat he spent 7 days to travel back. How much time would he need to sail the same distance down the Mississippi river on a raft?

LtP19

Appendix I February 25, 2020
The other day I heard about so-called #JLochallenge. That inspired me to two tweets.
1.  I wonder why there is no single celebrity in whole #America who will promote thinking/brain-development?
2. I'd like to join the bikini challenge, but that would be a disaster.
Instead I offer a #brainoohhh challenge. Anyone can pick one puzzle, solve it, and offer a new one. The last one had four pictures with different puzzles. The answers are after the pictures.

1. The first move is Knight goes d6 to h2.

2. The answer to the first problem is 1 and 2.
The answer to the second problem is 4.

3. The answer is 25 cm.

The problems were taken from some standard Russian books.
Th solutions are very simple. Theoretically every middle-school graduates has to be able to solve theses problems (even the chess one). However, I suspect that is not a case, because ... well, I have been writing on this matter for years. Just read one or two posts, for example:

No sign for improving math education soon.

or

Education Reform Needs a New Paradigm

Appendix II
Intelligence is an ability to design a solution to a problem one has never solved before, and express that using a language (including symbolic). BTW: this is what AI professionals do not want to admit. The most general approach for designing a solution is scientific thinking. One of the crucial features of it is learning from mistakes.
Teaching how to learn from mistakes separates common mass education from the actual/"elite" one.
Recently I saw a publication about a "three-problem intelligence test" invented by an MIT professor. Those problems are from my list, too, and they have nothing to do with intelligence, and everything  to do with having a good teacher.