Logic Riddles

1

Four men are trying to cross a small bridge. They can each individually cross it in 1, 2, 5, and 10 minutes respectively. To cross, they must carry a lantern to light the way, and at most two can cross at the same time (when two people cross it takes the longer time for both of them). Can they all get across in 17 minutes? (Remember they have to bring the lantern back for the other people to use!)

Solution for Number 1

2

Dissection: The picture below shows how to dissect the polygon into four congruent parts. Can you find the only way to dissect the same polygon into five congruent parts?

Solution for Number 2

3

Here's a problem that was used as the basis of a television show to illustrate the difference between the way a human mind approaches such a problem and the brute-force approach of a computer that finds the solution by trying all possible 40,320 different arrangements of the digits. Place the digits from 1 though 8 in the eight circles shown in the diagram, but with this restriction: no two digits next to each other in serial order may go in circles that are connected by a direct line. (For example: if 2 is placed in the top circle, neither 1 nor 3 may be placed in any of the three circles in the horizontal row beneath it because each of these circles is connected to the top circle by a direct line.) There is only one solution.

Solution for Number 3

4

Ten gnomes are about to be executed. Although they don't like the idea, they are each selfless and want to do anything (even by sacrificing themselves) in order to help their fellow gnomes. They are told what will happen to them: They will each be lined up single file, so that they are each facing the gnome in front of them. Each of them will be given a red or a white hat on their head, and from the back of the line (the gnome who can see everyone else) they will ask him to state his hat color, 'red' or 'white.' If he can state it corectly (he cannot see his own hat, only those in front of him), he is allowed to live. Knowing what is going to happen to them, they are allowed to deivse a strategy beforehand. How many peolpe can they guarantee to save, and what strategy will ensure this?
(There are NOT five reds and five whites necessarily!)

Solution for Number 4

5

A man has a 12 liter jug of beer, and wants to split it in half, but only has a 8 liter and a 5 liter jug. How can he do it?

Solution for Number 5

6

12 people say the following statements one after another: 1: There are no honest people in this room; 2: There is at most one honest person in this room; 3: There are at most two honest people in this room . . . . . . . . . . 12: There are no more than 11 honest people in this room. How many honest people are in the room?

Solution for Number 6

7

Three men go to spend the night at a hotel. They pay for a $30 dollar room, each giving $10 for their share. When they go to their room, however, the manager realizes that the room is on sale for $25, and gives $5 to the bagboy to return to the men. The bagboy goes to give back the five dollars, and when he does, the men take it, but give the bagboy $2 as a tip, thereby keeping one dollar each for themselves. However, one of the men is disturbed, remarking, "Hey, we each spent 9 dollars just now, since we got one back, which means $27 total, right? Plus the $2 we gave the bagboy, that's only $29! Where's the extra dollar?"

Solution for Number 7

8

One farmer bought a square piece of land, surrounded it with a fence, and signed with the naīve landlord a contract, under which the farmer had the right to perform several times the following operation: draw a straight line through any two points along the fence, take down the portion of the fence between those two point, and construct the same part of the fence symmetrically reflected in that line. Could the farmer increase the area of his land under this contract?

Solution for Number 8

9

There are three light bulbs in a room, and three light switches outside the room. You are outside, and want to match up which switch goes with which light bulb. You can only travel into the room once, and cannot come back in again. You can do anything you want upon entering the room. How can you set the situation so that you will know which switch goes with which light bulb?

Solution for Number 9

10

The code lock has three buttons with the numbers 1, 2 and 3 on them. The combination that opens the lock consists of three digits (the lock opens as soon as that combination is keyed in the right sequence). What is the least number of times that you have to press the buttons to break the code?

Solution for Number 10

11

A very long hallway has 1000 doors numbered 1 to 1000; all doors are initially closed. One by one, 1000 people go down the hall: the first person opens each door, the second person closes all doors with even numbers, the third person closes door 3, opens door 6, closes door 9, opens door 12, etc. That is, the n th person changes all doors whose numbers are divisible by n . After all 1000 people have gone down the hall, which doors are open and which are closed?

Solution for Number 11

12

While looking at the Pentagon building, what is the probability that you will see three of its sides? (not an aerial view)

Solution for Number 12

13

The plug of the computer cord has 7 contacts located in a circle. It plugs into the outlet, which has 7 corresponding holes. Is there any way to number the contacts on the plug and the holes on the outlet, so that at least one of the contacts would fit in the corresponding hole any time you plug in the cord?

Solution for Number 13

14

In a factory, there are ten sacks of goods, each with ten goods weighing 1 kg each (total 10 kg). A worker tells the quality control person that one of the sacks is lighter than the others, filled with ten .9 kg items, totalling 9 kg, instead of the normal 10 kg sacks. The quality control man decided that he could find the lighter sack with only one weighing. How did he do this?

Solution for Number 14