The Enterprising Art Dealer

A London art dealer purchased a painting for £60,000 and hung it in her gallery. Many people liked the painting very much and she was able to sell it in a few weeks' time for £70,000. The very next day after the painting was delivered, another customer inquired about the painting and claimed they would be willing to pay £90,000 for it if it were still for sale. The art dealer borrowed £10,000 from her partner and bought the painting back from the original customer for £80,000 and was then able to sell it to the second customer for the £90,000 that had been agreed upon.

How much profit did the art dealer make in her transactions?

Crossing the Bridge

Four men must cross an old bridge that spans a raging river. I'm not sure, but it might be the same river that the Victorian couples and the man with the tiger and goat needed to cross as well. The bridge is old and rickety and can only support two men crossing at once. To make matters even worse, it is pitch black and they have only one flashlight to share between them, which means that after two men have crossed one must return with the flashlight. Each of the men has differing abilities and some take more time to cross than the others. The times it takes for each man to cross are: 1 minute, 2 minutes, 5 minutes, and 10 minutes. When crossing in pairs, they can only cross as fast as the slowest man can go.

Can you find a way for all four men to cross in 17 minutes or less?

Three Squares in 2008

Here's another request from a reader:

"How can I write 2008 as the sum of three squares?"

There are four ways you can write 2008 as the sum of three squares, can you find all of them?

Simple Algebra

A reader of this page asks:

"If x²+y² = 36 and (x+y)² = 64, what is the value of x∙y?"

Help a fellow puzzle fan discover the values of x and y.

7 and 7 and 7 and 7 is 56

Using four 7s and any of the basic arithmetic operators (+, -, x, ÷) can you make 56?


7    7    7    7 = 56

Taking Notes

If six boys can fill up six notebooks in six weeks and four girls can fill up four notebooks in four weeks, how many notebooks can a class of twelve boys and twelve girls fill up in twelve weeks?

Change for a Dollar?

In the American money system, there are five coins in regular use. The penny is worth 1 cent, the nickel is worth 5 cents, the dime is worth 10 cents, the quarter is worth 25 cents, and the half-dollar is worth 50 cents.

If you use no more than 4 of any type of coin, how many different ways can you make change for 1 dollar (100 cents)?

5 Times 2 = 7?

Using only basic arithmetic operations make 7 out of five '2's.


2    2    2    2    2 = 7


You can use '+', '-', 'x', or '÷' between the '2's.

Odd Arithmetic

Find four consecutive odd numbers that add up to 80.

Find five consecutive odd numbers that add up to 85.

The Motel Room

Three businessmen are in Cleveland for a convention. Since they are on a budget, they decide to share a room at a motel that charges $30 per night ($10 per man). The motel manager is in a good mood that night and decides to reimburse some of the money. He gives the bell boy $5 and tells him to give it to the three men. However, the bell boy is dishonest and figures that you cannot divide $5 evenly among three men, so he gives back $1 to each man and keeps the other $2 for himself.

Now, the businessmen have each paid $9 for the room, or $27 all together, and the bell boy has $2, for a total of $29.

What happened to the other $1?

A Binary Crossnumber Puzzle

This puzzle consists completely of binary numbers, so all the characters needed to fill in the squares will be 0s or 1s. The crossword is a 4x4 square grid, so all numbers will be written in binary, with 4 digits; e.g., 1 will be 0001, 2 will be 0010, and 4, 0100. The NOT operation changes all 0s to 1's and all 1s to 0s; e.g., NOT(0110) is 1001 and NOT(1010) is 0101.

Rows (Across): 1. "2 Down" x 2 2. A triangular number 3. The cube of ("4 Down" - 2) 4. "3 Across" + "3 Down"

Columns (Down): 1. NOT "2 Across" 2. NOT "1 Across" 3. "2 Across" x 2 4. "4 Across" - "1 Across"

Needle in a Haystack

How many needles can you find in the haystack below? The word 'needle' may appear horizontally, vertically, or diagonally in any direction, but all six letters will appear in a straight line.


n e d e d
d e d e d l e l l
e e e e n n e e l e e
n n d e d l e d e e d n l
e l e e e e d e n n l d e
e e l n l e e e e n e d e d n
l l n n e e e e n d n e e e e
e e d e e l d e l e d d n d l
e e d e e l e d l n l l e e e
e n l e e e e e e d e d n l l
n n e e n n e n e e e e e e d
e e l d e e d d n n l e e l e
e d d l n l e l e e l n n e e


The Magic Keyring

Engrave numbers on 5 keys on a circular keyring so that the numbers on adjacent groups of keys sum to any value between 1 and 21 inclusively.

For example, 1,1,3,6,6 can sum up to any number between 1 and 17 (1=1, 1+1=2, 3=3, 3+1=4, 3+1+1=5, 6=6, 6+1=7, 6+1+1=8, 6+3=9, 6+3+1=10, etc).

Bobbing for Apples

Professor Egghead's secretary, Mrs. Canton, wanted to buy all the grocer's apples for a church picnic. When she asked how many apples the store had, the grocer replied, "If you add 1/4, 1/5, and 1/6 of them, that would make 37."

How many apples were in the store?

The Red Herring

A 'Red Herring' is a plot device used in literature to distract the reader away from the main event of the story by focusing on a minor event or describing characters in ways that go against our sense of the way those character should be. In cryptography, a red herring is a second hidden message that is intended to be discovered more easily so that the real message remains hidden to anyone who might intercept the transmission and break the red herring code. Only the intended receiver would know the key to unlocking the real message.

The cryptogram below, with two hidden messages, is a prime example of a red herring. One message is fairly easy to decipher, especially if you were able to decode an earlier puzzle that appeared here: http://puzzlepage.blogspot.com/2008/01/find-hidden-message.html. The second message, the one that's the real message, is hidden using a different code that has been made to fit in the same grouping of numbers. This is an extremely difficult cryptogram to solve, so feel free to ask for hints in the comment section.


21941648698194164869819416486981
54961847952716486981947648697358
39114467658829115524463869851941
76487962174268859915413638294575
51947682873991174467835921746687
82992113426384971634855658399727
12432613829431624856389791172446
83953124636885997711344766849911
44758746436849618496184961849618
49361849618898184961849618496184
69819416486981941648698194164869
81961635248698194164869819416486
89915214466889912144668899114466
88279911446688995114466889911446
75879618496188921246648691144666
89921347658591134764869871924164
86921354456289291314419885991234
61839518465768533281559123134362
84931546687899361547678297124312
44951746678897194362778135951543
64856618399613949711429889811444
48896919466819961882828694114914
49981941698618994964219181649644


Good luck!

I Want Candy!

Donna bought one pound of jellybeans and two pounds of chocolate for $2. A week later, she bought four pounds of caramels and one pound of jellybeans, paying $3. The next week, she bought three pounds of licorice, one pound of jellybeans, and one pound of caramels for $1.50.

How much would she have to pay on her next trip if she bought a pound of each of the four kinds of candy?

12 I in a F

Another reader of this page asks:

"I've been given a puzzle where I have to find words that fit in place of the single capital letters in this sentence:


There are 12 I in a F.

The single letters are to be replaced with words that start with the provided letter."


I'm sure most of you can figure it out soon enough--hopefully the reader who asked the question won't stub their toe in their haste to solve this little stumper.

Pigs in a Pen

Can you put nine pigs in four pens so that there are an odd number of pigs in each pen?

4 + 5 = 10?

In the figure below are four straight lines. Can you add five straight lines to the figure to end up with ten?

It's Hip to be Square

Arrange two of each of the digits 0 through 9 to form a 20 digit number. The number may not begin with 0. Then score the number as follows:

For every two consecutive digits that form a perfect square, score two points. For every three consecutive digits that that form a perfect square, score three points. A four digit square scores four points, and so on.

For example, if your number was 58738219024719503664, you would get two points for 49, two points for 36, two points for 64, and six points for 219024 for a total of 12 points. You may not count 036 as a three digit square.

What is the maximum number you can score?