6 + 5 = 9?

In the image above are six lines.  Can you add five new lines, different from the six original lines, to end up with nine?

The Three Beggars

A charitable lady met a poor man to whom she gave one cent more than half of what she had in her purse. The poor fellow, who was a member of the United Mendicants' Association, managed, while tendering his thanks, to chalk the organization's sign of "a good thing" to her clothing. As a result, she met many objects of charity as she proceeded on her journey.

To the second applicant she gave 2 cents more than half of what she had left. To the third beggar she gave three cents more than half of the remainder. She now had one penny left.

How much money did she start out with?

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?

Professor Egghead's Cuckoo Clock

On one of his trips to Switzerland Professor Egghead bought a handcrafted cuckoo clock that chimes on every hour and half hour mark. On whole hour marks the little birdie cuckoos once for each hour, and on half hour marks it cuckoos only once.

One night our favorite professor was wakened suddenly and realized that the clock had chimed but he did not know how many times. As he lay awake thinking about nothing in particular he heard the birdie cuckoo once and he started to wonder what time it was.

What is the longest amount of time Professor Egghead would have to lie awake before he knew for sure what time it was?

Five Men and Two Bridges

In the puzzle Crossing the Bridge, we met four people who needed to cross a bridge at night. In this puzzle there are five people who have to cross two sequential bridges at night. Like in the earlier puzzle, there are some hindrances:

The bridges can only support two people crossing at a time.

Each person has a different speed in which they can cross: 10 minutes, 7 minutes, 5 minutes, 2 minutes, and 1 minute.

They only have two flashlights to share between them. A pair of people can share one flashlight, which means there can be one pair of people on each of the two bridges at the same time.

If the short time it takes to get from the first bridge to the second can be ignored, what is the shortest amount of time it will take for all five people to cross both bridges?

3 F in a Y

A fellow Puzzle Page reader has been told that there are 3  F in a Y.

Can you replace F with a word that starts with the letter 'F' and replace Y with a word that starts with the letter 'Y' to solve the puzzle?

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.

How Old Are They Now?

This puzzle is meant for all the people who had trouble with age problems during high school algebra. In fact it might finish age problems all together. The next time you are asked to solve a problem about Dick being four times older than Fred was last Thursday, etc., pull this one out of your pocket.

I'm not even sure if this one has a real solution or if it's only meant as a joke, but either way it will keep you busy (and baffled!) for a very long time.

Ten years from now Tim will be twice as old as Jane was when Mary was nine times as old as Tim. Eight years ago, Mary was half as old as Jane will be when Jane is one year older than Tim will be at the time when Mary will be five times as old as Tim will be two years from now. When Tim was one year old, Mary was three years older than Tim will be when Jane is three time as old as Mary was six years before the time when Jane was half as old as Tim will be when Mary will be ten years older than Mary was when Jane was one-third as old as Tim will be when Mary will be three times as old as she was when Jane was born.

How old are they now?

The 'Tree'mendous Apple Orchard

A certain farmer wanted to create a special orchard in the vacant field next to his house. He had been given ten special apple tree saplings: a Pink Lady, a CandyCrisp, a Fuji, a Cameo, a Granny Smith, a McIntosh, a Jonagold, a Red Delicious, a Senshu, and a Winesap. After careful consideration and planning it was decided that the apple trees would be planted so that there were five rows of trees with four trees in each row.

When he told his neighbors about his plan they all laughed and told him it was impossible to plant ten trees so that you have five rows of trees with four trees in each row.

The following year this is what his neighbors saw:

Click on the picture for a larger image


A few years later the same farmer was given six more apple trees: a Stayman, a Fortune, a Cortland, a Honeycrisp, a Macoun, and a Northern Spy. Six trees wasn't enough to create another star pattern of trees so he came up with a new plan. He changed the planned orchard and planted the six new trees so that all sixteen apple trees were placed in fifteen rows with four trees in each row.

What did the farmer's apple orchard look like when he was done?

Those Incredible Colored Socks

Professor Egghead woke up one morning and started dressing for a day in the office. He reached into his sock drawer and felt that there were four individual socks. He knew that two of those socks were black, one was white, and one was green. He grabbed two at random and put them on before leaving for work.

If one of the socks he was wearing was black, what is the probability that the other one was also black?

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.

The Missing Tile

Here's another favorite of mine. I think this one, above most other puzzles, can truly be described as a mind bender.

In the diagram below (click on the image to get a larger version) you see two figures made up from the same pieces. In the upper figure the colored pieces are arranged so that the area of the figure is (13 x 5) ÷ 2 = 32.5 tiles. In the lower figure, the same colored pieces have been rearranged so that the area of the figure is (13 x 5) ÷ 2 - 1 = 31.5 tiles (the -1 is for the missing tile above the number 8.)



This is not an optical illusion; the grid lines are there to help demonstrate that all the squares are uniform. Feel free to print out a copy of the picture, cut out the colored pieces in one of the figures and lay them out on top of the other figure to prove that they are indeed the same size.

How can it be possible to disect a polygon, rearrange the order of the pieces and end up with less (or more) space than was used before?

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)?

More Barrels and More Pellets

In the puzzle Barrels Full of Pellets you were asked to find a way to discover which single barrel contained pellets that were slightly heavier than all the other barrels. This brain teaser is based on that one, but is considerably more difficult:


You are presented with ten barrels of pellets, but this time you are told that some or all *may* have 2 gram pellets and the rest have 1 gram pellets. You are given a scale for measuring and you are only allowed to take a measurement one time.

How do you find out which of the ten barrels have 1 gram pellets and which of the barrels have 2 gram pellets?

Hobos and Cigars

A certain hobo can make cigars from discarded cigar butts. He finds that with 5 cigar butts he can make one whole cigar.

One month he collects 25 butts. How many cigars can he make?