Leap Babies

I'm sure you're aware that a year is defined as the number of days it takes for the Earth to revolve about the sun. That time is not evenly divisible into the number of hours it takes for the Earth to revolve on its axis, which is how we define the length of a day. What that all means is that instead of being exactly 365 days, a year is closer to 365¼ days.

In order to account for that extra ¼ day, we add an extra day to the calendar every four years and call that year Leap Year and the extra day is sometimes called Leap Day, which falls on February 29 in a Western calendar.

Now here's the puzzle for today: Assuming a regular birthrate, what percentage of the population celebrates their birthday on February 29?

What Color was the Bear?

A reader asks, "If a bear woke up, and began to walk, and every way he walked was south, what color was the bear and why?"

Hunters and Cabins

Here's a difficult Logic Puzzle that comes from a 1975 Creative Computing magazine. It isn't easy; it could swallow up a day of your time, even a week, but it will take more than an hour.

The following 15 clues are all you need to solve this Logic Problem:


1. There are five hunting cabins on a lake. Each cabin is a different color, and is inhabited by a man of a different nationality, each drinking a different kind of liquor, firing a different brand of shotgun shell, and shooting a different duck.

2. The Englishman lives in the red cabin.

3. The Pole shoots only bluebills.

4. Bourbon is drunk in the green cabin.

5. The Finn drinks beer.

6. The green cabin is immediately to the right (your right) of the brown cabin.

7. The hunter who uses Winchester shells shoots mallards.

8. Remington shells are shot in the yellow cabin.

9. Brandy is drunk in the middle cabin.

10. The Norwegian lives in the first cabin on the left.

11. The man who buys Federal shells lives in the cabin next to the cabin of the man who shoots red heads.

12. Remington shells are used in the cabin next to the cabin where canvasbacks are shot.

13. The hunter who shoots Western shells drinks gin.

14. The Irish man loads up with Peters shells.

15. The Norwegian lives next to the blue cabin.

Your mission, should you decide to accept it, is to figure out who drinks Scotch and who shoots the teal.

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?

A Different Kind of Sudoku

Here's a sudoku challenge of a slightly different sort. In the 5x5 grid shown below, write (x,y) pairs, with x and y ranging from 1 to 5 inclusively, with the stipulation that x and y values cannot be repeated in any row, column, or diagonal.

For instance, if you write the (x,y) pair (1,3) in the top left cell, then you can not have any other pairs with an x value of 1 or a y value of 3 in the top row, the left-most column, or the main diagonal that runs from the top left to the bottom right.

This puzzle can be solved fairly quickly and is not quite as difficult as it may seem.


Click on the picture for a larger version

Behind the Green Door

You are a captive in a far away land. The king offers you your freedom if you can pass the following test:

You are placed in a room with two doors. Behind one door is a ferocious tiger, behind the other is your escape. 30 feet above each door is a window where a man is sitting. One man always tells the truth, the other is a constant liar. You may ask only one question.

What one question do you ask and to which man do you pose that question so that you are assured to reach freedom and not be eaten by the tiger. Remember; you don't know which man is honest and which one lies.

Circling a Chess Board

On a standard chess board with individual squares that measure two inches on each side, what is the largest circle that can be drawn so that the circumference lies only on black squares?


Click on the image for a larger view

1 + 1 = 10?

A reader of this page asks,

"When does 1 plus 1 equal 10?"

I know the answer, do you?

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)?

Artful Arithmetic

Professor Egghead had a student who was not very good with fractions and thought she had stumbled upon a quick way of discovering which of two fractions was the larger.

When she was asked to find the larger between 2/5 and 3/7 she simply subtracted the numerator from the denominator in each fraction, replacing them with 2/3 (2/(5-2)) and 3/4 (3/(7-3)) respectively, which she then replaced with 2/1 and 3/1, using the same method, and concluded that the first, 2/5, was the smaller.

Professor Egghead was impressed with her method. Was her method valid or was it complete nonsense and her correct answer only a lucky coincidence.

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 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!