**Some Lateral/Math Problems**

For a number of years (long time ago), I was teaching a Problem-Solving
course to ITT-Technical students (in addition to algebra, geometry, and
physics). 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.

**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 4-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?

**LtP**

**1**

**8**

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?

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.

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.

**Appendix**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.

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