Longfellow

Half-way up the hill, I see thee at last, lying beneath me with thy sounds and sights -- A city in the twilight, dim and vast, with smoking roofs, soft bells, and gleaming lights.

Two Bodies in One

Two bodies have I
Though both joined in one.
The more still I stand,
The quicker I run...

Take as Much as You Like

I am nothingness, and the more you take from me, the bigger I get.

A Counting Problem

How many terms are contained in (a + b + c)²⁰ .

Your Daily Dose of Word Puzzles

1.
DAYDAYOUT

2.
THOUGHT AN

3.
SEARCH

AND

4.
222222222day

5.
VIT_MIN

1 END 3 END 5 END 7 END 9 END

Can you tell what each of these five word puzzles mean?


1.
soiudte


2.
S   M
E   U
O   S
G   T
T   C
A   O
H   M
W   E


3.
ABCDEFGHIJKLMNOPQRSTUVWYZ
QQQQQQQQQQQQQQQQQQQQQQQQQ


4.
oz
e


5.
1 END 3 END 5 END 7 END 9 END 

Tick-Tack-Toe Game

Tick-Tack-Toe

David and Angela play a game of tick-tack-toe. In this game, the players try to get three circles or three crosses in a row (horizontal, vertical, or diagonal).

They follow the following rules:

A player always tries to win: if a player can place his own symbol (X or O) in a row which already contains two of his own symbols, he will do so.

A player always tries to avoid that his opponent wins: if a player can place his own symbol (X or O) in a row which already contains two of the symbols of his opponent, he will do so.

Of course, the first rule has precedence over the second rule, because the game can be won in this way.

In the game shown on the right, 6 moves have been done. David plays with crosses (X) and Angela plays with circles (0). However, we don't know who started the game.

Who will win this game?



If you're like me, you may be having trouble seeing the image of the board I tried to create. So here's a more basic image:
O | O |
----------
O | X |
----------
X | X |

Moon Cable

A large space agency has decided to build a base on the moon. For this purpose, a cable must be laid around the moon's equator. When the cable is laid, it turns out to be 1 meter short. In a quickly arranged meeting, it is decided to investigate the possibility to lay the whole cable in a groove.

How deep does the groove need to be to make this work?

The agency's director considers digging a groove, no matter how deep, around the entire circumference is too expensive. He suggests to lay the whole cable just a bit north of the equator. How many meters north of the moon's equator should the cable be laid to settle the problem of the lacking 1 meter of cable?

Golden Opportunity

It has a golden head
It has a golden tail
but it hasn't got a body.

What is it?

Help Win an iPad2

Hi all,
I never do this, but I'd like to make a personal appeal.  My daughter was entered into a contest to win an iPad2.  She painted a pottery piece at PYOP for her teacher at school.  The lady who runs it liked it enough to enter it into her summer contest to win an iPad2.  At six years old, that would be quite a prize.

If you have a facebook account, please head on over to the PYOP album (https://www.facebook.com/media/set/?set=a.10150194490771739.307688.40310146738) and like here photo (the one with the butterfly).  In case you're wondering, it's a dunk mug.  You can put cookies down at the bottom, for dunking!

Thanks for helping out!  We'll be back to our puzzles on Monday.  Happy father's day to all the dads out there!

Ants on a Board

There are 100 ants on a board that is 1 meter long, each facing either left or right and walking at a pace of 1 meter per minute.

The board is so narrow that the ants cannot pass each other; when two ants walk into each other, they each instantly turn around and continue walking in the opposite direction. When an ant reaches the end of the board, it falls off the edge.

From the moment the ants start walking, what is the longest amount of time that could pass before all the ants have fallen off the plank? You can assume that each ant has infinitely small length.

Reindeer Line

There are nine reindeer, all in a line.  Can you figure out the order?

Comet behind Rudolph, Prancer and Cupid. Blitzen behind Cupid and in front of Donder, Vixen and Dancer. Cupid in front of Comet, Blitzen and Vixen. Donder behind Vixen, Dasher and Prancer. Rudolph behind Prancer and in front of Donder, Dancer and Dasher. Vixen in front of Dancer and Comet. Dancer behind Donder, Rudolph and Blitzen. Prancer in front of Cupid, Donder and Blitzen. Dasher behind Prancer and in front of Vixen, Dancer and Blitzen. Donder behind Comet and Cupid. Cupid in front of Rudolph and Dancer. Vixen behind Rudolph, Prancer and Dasher.

This one is from Kevin.

Generous Buzz

When Buzz gathered his 2001 records for his CPA, he found that he had made six donations, each for a different amount of money and totaling $1500, to six local youth sports teams, including a softball team. Given the data below, can you find how much in sports deductions Buzz has for 2001: the contribution to each team and the sport the team plays?

1. Buzz donated twice as much to the basketball team as he did to the Knights.
2. The contribution to the Comets was less than that to the football team.
3. For his donation to the soccer team, which was $50 more than he gave the Rovers, the soccer team advertised Buzz's gas station on the back of their jerseys.
4. The Lions got $150 more from the service station operator than the baseball team did.
5. The smallest donation of the six was for $50.
6. The Hawks received twice as much money from Buzz as the soccer team.
7. Before actually seeing the receipts again, Buzz thought that his largest donation had been $600 and that he had given the hockey team $250; he found that the largest contribution was for less than $600 and that the hockey donation was for less than $250.
8. Buzz gave the Knights $50 more than he gave the Devils.
9. The largest donation wasn't the one to the youth basketball team.

Six of One

The expression, "Six of one, half a dozen of another," is commonly used to indicate that two alternatives are essentially equivalent, because six and a half dozen are equal quantities. But are "six dozen dozen dozen" and "a half dozen dozen dozen" equal?

There are 5 ships in a port

The greek ship leaves at six and carries coffee.
The ship in the middle has a black chimney
The English ship leaves at nine.
The French ship with a blue chimney is to the left of a ship that carries coffee.
Right to the ship carrying cocoa is a ship going to Marseille.
The Brazilian ship is heading for Manila.
Next to the ship carrying rice is a ship with a green chimney.
A ship going to Genoa leaves at five.
The Spanish ship leaves at seven and is to the right of the ship going to Marseille.
The ship with a red chimney goes to Hamburg.
Next to the ship leaving at seven is a ship with a white chimney.
The ship on the border carries corn.
The ship with a black chimney leaves at eight.
The ship carrying corn is anchored next to the ship carrying rice.
The ship to Hamburg leaves at six.


Which ship is going to Port Said?
Which ship is carrying the tea?

Teacher is so Smart

After studying roman numerals for a short time, the teacher had given the class some free time.  Sally's teacher walked up to her desk and saw that she had written:

XI + I = X

on her paper.

He was quick to point out her mistake.  Sally protested, saying she had it right.  After demonstrating what she meant, the teacher apologized and moved on.

What did Sally point out?

Helen and Who Are Not Very Close

Yesterday evening, Helen and her husband invited their neighbours (two couples) for a dinner at home. The six of them sat at a round table. Helen tells you the following:

1. Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna.
2. Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband.
3. Jim sat on the left of the woman who sat on the left of Roger.
4. I did not sit beside my husband.

What is the name of Helen's husband?

Random Walk

A drunk leaves a bar (rather forcefully).  After standing up and dusting himself off (rather unsuccessfully), he decides to walk home.  Unfortunately for him, he has no idea where home is and has no way of deciding which way to go.  He is on a street traveling east-west only, making things simpler for him.

With each step, he's just as likely to turn around and walk back in the direction he came from.  After 20 steps, how likely is it he will be back where he started from (right in front of the bar)?

Time to Play

It goes up, but at the same time goes down. Up toward the sky, and down toward the ground. It's present tense and past tense too, come for a ride, just me and you.

What is it?

Split the Tab

You've been out to a restaurant with a group of people from work. The bill is now on it's way. Time for either a bit of philosophy/game theory. What's the best way to handle the bill? You have three choices: Split the bill evenly, pay for what you ordered, or got to the trouble of asking for separate checks?

For a good write up on the problem, try mindyourdecisions.

Not Exactly Chicken Nuggets

On a nice summer day, two tourists visit the Dutch city of Gouda. During their tour through the center they spot a cosy terrace. They decide to have a drink and, as an appetizer, a portion of hot bitterballs. The waiter tells them that the bitterballs can be served in portions of 6, 9, or 20.

What is the largest number of bitterballs that cannot be ordered in these portions?

Class is Almost Over

The gentlemen Dutch, English, Painter, and Writer are all teachers at the same secondary school. Each teacher teaches two different subjects. Furthermore:

• Three teachers teach Dutch language
• There is only one math teacher
• There are two teachers for chemistry
• Two teachers, Simon and mister English, teach history
• Peter doesn't teach Dutch language
• Steven is chemistry teacher
• Mister Dutch doesn't teach any course that is taught by Karl or mister Painter.

The Question: What is the full name of each teacher and which two subjects does each one teach?

In case anything has been missed:
The four first names are Karl, Peter, Simon, and Steven
The last four names are Dutch, English, Painter and Writer.
The classes are Chemistry, Dutch, History and Math.