Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math

High School Archive


This page:
  puzzles checkmark

  Dr. Math

See also the
Dr. Math FAQ:
  classic problems


About Math

   basic algebra
   linear algebra
   linear equations

Complex Numbers

Discrete Math

Fibonacci Sequence/
  Golden Ratio

     conic sections/
     coordinate plane
   practical geometry

Negative Numbers

Number Theory

Square/Cube Roots


Browse High School Puzzles
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to frequently posed puzzles:
    1000 lockers.
    Letter+number puzzles.
    Getting across the river.
    How many handshakes?
    Last one at the table.
    Monkeys dividing coconuts.
    Remainder/divisibility puzzles.
    Squares in a checkerboard.
    Weighing a counterfeit coin.
    What color is my hat?

Change for a Dollar [11/05/1999]

Checkerboard Rectangles [03/24/2003]

Choosing 3 of 6 Colors [03/03/2000]

Circle Packing [01/22/2001]
If circles packed in a 100 by 100 square are repacked so that the centers of any three tangent circles form an equilateral triangle, what is the maximum number of additional circles that can be packed?

A Circular Massacre [09/25/1998]

Claim the Last Flag [10/25/2002]

Clock Hands and Hours Worked [01/29/2003]

Clock Hands Diametrically Opposite [10/10/2001]

Clock Hands Trisecting Face? [04/05/1999]
At what time (if any) do the three hands of a clock trisect its face?

Closest Palindromic Dates [02/07/2000]
Using the abbrevation date.month.year, what are the two palindromic dates closest together in the 1900s?

Cockroach Traveling Along an Elastic Tightrope [05/15/1998]
Finding the harmonic series in a problem of related rates.

Coconut and Monkey Puzzle [12/18/1997]
How many coconuts were in the original pile?

Coconut Piles [10/12/1998]

Coconuts, Forwards and Backwards [02/02/2010]

Coffee or Tea? [07/09/2001]

Coin Patterns [08/26/2003]



Connecting the Boxes [12/28/1998]

Constructing a Conditional Table [04/14/1998]

Counterfeit Coin Challenge [05/12/2007]
In a set of 13 coins, either zero or two of them are counterfeit and are lighter. You must identify the counterfeit coins, if any, after four or fewer weighings on a balance scale.


Counting Rectangles [05/23/2001]
How can I find the number of different rectangles in a square grid containing "c" columns and "r" rows?


Counting Triangles [05/27/1999]
In a large triangle with 36 small ones inside, how many triangles are there in all?

Covering a Checkerboard after Removing a Random Square [05/11/2008]
Use mathematical induction to prove that for any positive integer n, if any one square is removed from a 2^n x 2^n checkerboard, then the remaining squares can be completely (and exactly) covered with L-shaped pieces composed of three squares.

Criminal Logic Problem [02/19/2005]

Crossing a Desert with 45 Watermelons [07/08/1998]
A boy carries 45 watermelons across a 15 mile desert, 15 at a time, eating 1 per mile. What is the most he can carry to the other side?

Crossing the Bridge [05/12/1997]
Four men want to cross a bridge but only two may cross at a time...

Crossing the Desert [05/22/2001]

Cryptography without Numbers [12/07/2003]

Crypto-Number Puzzle [01/21/1997]



Dartboard Scoring [03/01/1999]
Find the highest score you cannot get with the center worth 9 points and the outer ring worth 4.



Difference of Two Cubes [05/24/2001]
The difference of two cubes is 56,765. What two positive integers satisfy this condition?

Digital Clock Lights [06/29/1998]
If the only light source in a room is a digital alarm clock (red LEDs), at what time is the room the darkest? Lightest?

Digit Reversal Trick Explained [03/23/2001]


Search the Dr. Math Library:

Search: entire archive just High School Puzzles

Find items containing (put spaces between keywords):
Click only once for faster results:


parts of words whole words

[Privacy Policy] [Terms of Use]


© 1994-2015 Drexel University. All rights reserved.