How Old is she Now?

Nine years ago Karen was in her prime, eight years ago she was a power of a prime, and last year Karen was really odd.

How old is Karen now?

Dodecahedron

This is an extremely difficult problem and may take up days of your time to figure out.

A regular dodecahedron has twelve pentagonal sides and twenty vertices. Assuming that one face is in the X-Y plane with an edge along (0,0,0) to (0,1,0), what are the coordinates of the remaining 18 vertices?




Image created using Robert Webb's Great Stella software: http://www.software3d.com/Stella.html

Dropdown Puzzle

These puzzles are sometimes called droplines or quotefalls. Fill in the squares with the letters found in the column in the top part of the diagram. When correctly filled out you will see a quote.

Click on the picture for a larger view.

Still the same...

A reader asked the following puzzle:

"I have five letters. If you take the first and the last I will still be the same. Even if you take the middle letter I will be the same as before. What am I?"


Can you guess the correct answer?

O T T F F S S E

A reader wonders what the next letter in the following series should be:

O T T F F S S E ...

Can I count on you to help them out?

The Twins' Birthdays

A young woman celebrated her birthday on the anniversary of her birth date. Two days later her twin sister celebrated her birthday on the anniversary of her birth date.

How can this be true?

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?

The Puzzle Page Conundrum

The title of this blog page, The Puzzle Page, is written using nine distinct letters: A, E, G, H, L, P, T, U, and Z.

Can you arrange these nine letters in a 3x3 grid so that, starting with the letter T, and moving one square at a time you trace a path that spells out the name The Puzzle Page?

You may move one square orthogonally or diagonally and you may stay on the same square for both instances of the letter Z.


There is more than one solution. How many can you find?

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?

The Five Legged Lamb

Abraham Lincoln once asked, "How many legs does a sheep have if you call its tail a leg?"

What do you think the correct answer is?

A Fruity Problem

Professor Egghead's nephew spent a summer working as a stockboy for a large grocery store. It was a rather unusual grocery store, however, and they had a very strange way of arranging the fruit in the fresh produce area.

In one group you would find any of the following fruits:
apple, banana, grape, and orange.

In a different area you would find fruits like:
mango, nectarine, peach, and pear.

One day a new crate of fruit arrived and the young man wasn't sure where to put it. Where would you put a crate labeled strawberry?

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?

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?

I Like Ike Calendar

In 1952, Professor Egghead's father voted for Dwight Eisenhower for US President and had kept the calendar as a keepsake. Recently, Professor Egghead was going through some of his father's keepsakes and discoverd this calendar from 1952 and noticed that all the dates in 1952, which was a leap year, coincided exactly with the dates in 2008, which is also a leap year.

This made the professor wonder, how many different calendars would you need to have in order to represent every possible combination of yearly calendar?

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?

A Crossnumber Puzzle

Use the clues to fill in this crossnumber puzzle.

Clues
Across	Down
1. The cube of a whole number	1. A number that is unchanged if the digits are reversed
5. The number of square inches in a square yard	2. A prime number.
6. The number of cubic inches in a cubic foot.	3. The number of feet in a mile.
7. The number of millimeters in a meter.	4. The number of seconds in an hour.