Logic PuzzlesBreak out Session and Resources

Ph.D. Training – Published 03.21.2008Piled Higher and Deeper by Jorge Cham www.phdcomics.comInterviewers know if you’ve seen problems before.They're interested in seeing your thought process – not memorization skills

AgendaFour Logic PuzzlesResources

Ground Rules

If you know the solution already don’t say it – instead try to think of the process you would use to solve to problem

Entertain all thought processes – (even if you know it’s wrong) If you were perfect in your thought process these

exercises would be pointless

Keep some notes on each problem so we can compile them and share

17 Minute Bridge ProblemCommon, shows up in many forms, even a games devoted to it

The Rope Bridge

Four people need to cross a rickety rope bridge to get back to their camp at night.

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. Campers{w,x,y,z} = {1,2,5,10}mins

How do the campers make it across in 17 minutes?

Thought Process (Attacking the problem)

Solution (Extra Resources)

http://www.novelgames.com/flashgames/game.php?id=55 30 minute version – more people

1. (w) & (x) Cross with Torch (2 min)

2. (w) Returns with Torch (1 min)

3. (y) & (z) Cross with Torch (10 min)

4. (x) Returns with Torch (2 min)

5. (w) & (x) Cross with Torch (2 min)

Total 17 min

Dealing with Numbers

Estimation and Precision

Problem 1 (Estimation) How many golf balls can fit in a school bus?

Problem 2 (Precision) Lay 2 quarters on a flat surface so that their edges

are in contact. Hold one still and roll the other one around it. How many rotations does the moving quarter make?

Thought Process (Attacking the problem)

Solutions

One of many solutions: Assume Bus is

50 balls tall 50 balls wide 200 balls long

50x50x200 = 500K balls

Quarters: The intuitive straight line answer is 1

e.g. if the quarter rolled along the same linear distance as the circumference of the other quarter the answer is 1

The correct answer (due to the rotation around the original quarter) is 2

AssociationSeen in interviews, LSAT, MCAT tests etc.

There are 5 houses in 5 different colors. In each house lives a person of a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. Using the clues below can you determine who owns the fish?

The Brit lives in a red house. The Swede keeps dogs as pets. The Dane drinks tea. The green house is on the immediate left of the white house. The green house owner drinks coffee. The person who smokes Pall Mall rears birds. The owner of the yellow house smokes Dunhill. The man living in the house right in the middle drinks milk. The Norwegian lives in the first house. The man who smokes Blend lives next door to the one who keeps cats. The man who keeps horses lives next door to the man who smokes Dunhill. The owner who smokes Blue Master drinks beer. The German smokes Prince. The Norwegian lives next to the blue house. The man who smokes Blend has a neighbor who drinks water.

Thought Process (Attacking the problem)

THE GERMAN OWNS THE FISH

Nationality

Norweg Dane Brit German Swede

Color Yellow Blue Red Green White

Beverage Water Tea Milk Coffee Beer

Smokes Dunhill Blend Pall Mall Prince Blue Master

Pet Cats Horses Birds Fish Dogs

MISC

Change the position of just one of the words below so that all the words are in an alphabetical sequence: llama phoenix hyena alligator beaver elephant

tortoise antelope

A ship is docked in the harbor. Over the side hangs a rope ladder with rungs a foot apart. The tide rises at a rate of 9 inches per hour. At the end of six hours, how much of the rope ladder will still remain above water, assuming that 9 feet were above the water when the tide began to rise?

Thought Process (Attacking the problem)

THINK ABOUT THE PROBLEM

Antelope: move it from the end to the beginning, the initial letters will then spell ALPHABET.

Still 9 feet because the ladder will rise with the ship!

These puzzles taken from brainbashers.com

Resources

Online Resources

http://www.techinterview.org/

http://tiny.cc/BNao2 (Handling Brainteasers and Logic Questions in an Interview)

http://tiny.cc/EM2vw 10 steps to solving any sizing question

http://www.brainbashers.com/puzzles.asp

http://www.pzzls.com/

http://www.puzzle.dse.nl/logical/index_us.html

http://brainden.com/logic-puzzles.htm

http://www.puzzles.com/projects/LogicProblems.html

Audience

What brainteasers have you heard are common?