# Web Puzzles

## Canopus

There is a number made of eleven tens of thousands, eleven thousands, eleven hundreds, and eleven units?

What is that number?

### Canopus Puzzle Solution

A nice and simple sum does the trick.…
 110,000 + 11,000 + 1,100 + 11 = __________ 122,111

## Deneb

She was an absent minded one, forever seeing things that interest her intellilect and hold her in thought for hours on end. On this particular time, she saw a curious symbol, her mental processes setting formulating a problem to solve.

Starting at any point, how can you draw the whole symbol by tracing along the lines and never tracing along the same line twice?

## Visit At The White House

"This," started the guide, "is the Buttons Room."

The Druggar of Bongo Ghango - the chief of a large country by the River Ghango - looked around. "It's a nice room, but where are the buttons? The only ones I see are, ahem, the ones on your shirt."
"Your Highness. The buttons, which could start a nuclear armageddon in a matter of seconds, are there, behind that panel," replied the guide, while pointing at a large panel at the end of the room.
"How can that be??? Why? Anybody - a madman, for example - could come here and press those terrible buttons?"

"Your Highness, it is very safe actually: for every button there is a slot, where a magnetic card must be inserted to activate the corresponding button. No card, no button. To launch the missiles, all buttons must be activated and pressed, and only a handful of people have the magnetic cards, and each card contains a different code from all the other ones."

"But it's the same thing! Any of these persons could go completely ballistic and start a nuclear war."
"In that case, the only dangerous man is the President of the United States, as he is the only person that holds all the codes, which would allow him to press all the buttons. The other people that hold some codes are the Vice-President of the United States, the President of the Senate, the Secretary of State, the Chief of the Armed Forces, and the Dean of Harvard University. Each of these gentlemen holds an incomplete set of magnetic cards, and the distribution of the codes is such that, if the President of the United States is not available, the entire set of buttons can be activated by the Vice-President, together with anyone of the other four men. If both the President and the Vice-President of the United States are unavailable, the buttons can still be activated by any three of the other four men. Therefore, to launch the missiles, it is needed either the President, or the Vice-President plus anyone of the other four men, or any three of the other four men."

"What if someone tried to press randomly many buttons, one after the other?" asked the Chief.
"Nothing would happen with the missiles, but the room would fill up with a narcotic gas, and an alarm would alert the guards and the CIA."

"So, how many buttons are there, and how are they distributed between the Vice-President and the other four personalities?"

And that's the question we'll ask the reader: what is the minimum number of buttons, and how are they distributed?

### Visit At The White House Puzzle Solution

There are 7 buttons. The magnetic cards, as held by the six persons, and marked with an X, are distributed as follows:
Person Buttons
President X X X X X X X
Vice President X X X X X X -
President of Senate X X X - - - X
Secretary of State X - - X X - X
Chief of Armed Forces - X - X - X X
Dean of Harvard - - X - X X X

## Visit At The Kremlin

"This," explained Colonel Nevskij to the Druggar of Bongo Ghango - chief of a large country by River Ghango - "is the Buttons Room."

"I've seen a room like this in Washington," replied the big Chief, smiling with satisfaction, "there too, you couldn't see a single button. The only ones I can see here are, uh.. hehe, the ones on your uniform, Colonel!"

"Ahah, comrade Druggar likes joking. But the buttons are here," replied the Soviet, pointing at a large panel at the end of the room, "they are behind that panel."

"A very large panel," observed the Chief, "much larger than the one at the White House: I presume there are more buttons here."

"Of course, comrade Druggar: in America, only a bunch of opportunistic capitalists has a saying in the big decisions, while here, uh, here is different: the entire Soviet community, through its representatives, takes part in the decision process of the Union."

"Any citizen could then come here and press the buttons?"

"Err, no, not exactly. If I tried to do it, the room would fill up with narcotic gas, an alarm would set off, and... Well, no need to talk about that. For each button there is a slot, into which a magnetic card must be inserted, to activate the corresponding button. Therefore, no card, no button. To launch the missiles, every button must be activated and pressed, and only a handful of comrades holds the magnetic cards, which of course, each of them has a different code from the others. The personalities holding the cards are the Secretary of the Communist Party, the President of the Praesidium, the Chief of the KGB, and five comrades, Heroes of the Soviet Union. The distribution - and here is the originality of our system - is such that the Secretary of the Party holds the complete set of codes, and so he can launch the missiles by himself; if the Secretary is not available, the missiles can be launched by the President of the Praesidium together with the Chief of the KGB, or by anyone of these two, together with any two of the five Heroes of the Union. If - Marx forbid - the Secretary, the President, and the Chief have all been victimised by an imperialistic attack, our nuclear response can be initiated by any four of the five Heroes of the Soviet Union; any four of them would be sufficient to have the entire set of magnetic cards to activate the buttons."

"So, how many buttons are there?" asked the Chief.

What is the minimum number of buttons, and how are they distributed?

### Visit At The Kremlin Puzzle Solution

There are 20 buttons. This is because there are 10 combinations of Heroes in pairs of 2, and this is multiplied by 2 because these combinations have to be mapped to two different persons (the President of the Praesidium or the Chief of KGB). The magnetic cards, as held by the eight persons, and marked with an X, are distributed as follows:
Person Buttons
Secretary of Party X X X X X X X X X X X X X X X X X X X X
President of Praesidium X X X X X X X X X X X X X X X - - - - -
Chief of KGB - - - - - X X X X X X X X X X X X X X X
1st Hero X X X X - - - - - - - X X X X X X X X -
2nd Hero X X X - X X X X - - - - - - X X X X - X
3rd Hero X X - X X - - X - X X - - X - X X - X X
4th Hero X - X X X - X - X - X - X - - X - X X X
5th Hero - X X X X X - - X X - X - - - - X X X X

## Frogs

Four ladies are facing each other. Each one of them speaks twice. One of those statements is truth, the other is a lie.

Amanda:
"I am a frog but I look like a princess."
"There are at least three frogs between the four of us."

Barbara:
"I'm a princess."
"Corinna always lies."

Corinna:
"There is only one frog here."
"I'm a frog that looks like a princess."

Deborah:
"Two of us are frogs."
"I'm a princess."

Are there any frogs? If so, what are their names

### Frogs Puzzle Solution

The only frog is Amanda. The table below shows, on the left, all possible combinations of frogs (X stands for frog, - stands for non-frog), while on the right pane there is the control of the truthfullness (T for true, F for false) of each given statement, for each combination of frog population. The only combination where every girl tells one true statement and one false one, is the emphasised row. Hence, there's only one frog, and that's Amanda.
Possible Frogs Statement
A B C D A B C D
- - - - F F T F F F F T
- - - X F F T F T F F F
- - X - F F T F T T F T
- - X X F F T T F T T F
- X - - F F F F T F F T
- X - X F F F F F F T F
- X X - F F F T F T T T
- X X X F T F T F T F F
X - - - T F T F T F F T
X - - X T F T F F F T F
X - X - T F T T F T T T
X - X X T T T T F T F F
X X - - T F F F F F T T
X X - X T T F F F F F F
X X X - T T F T F T F T
X X X X T T F T F T F F

## Creative Lamps

These unusual and very interesting lamps are developed by the Studio Cheha (Tel Aviv, Israel) and they all share one interesting secret which is not immediately visible. See the full post and find out!

The thing is that they are all flat, though it may seem otherwise.  Look at them once again and discover that these objects are  2-dimensiona!:)

## Swapping Art

"Four drawings by Max Ernst are worth as much as five sketches by Magritte, do you agree?" asked Giorgio Parconi, an Italian art dealer. He was tired of arguing over this.

"D'accord!" agreed Cesar Blanchard, who was the director of a Parisian art gallery.

"And we all agree that two sketches by Magritte plus one drawing by Ernst are worth as much as two paintings by Bacon. Right?"

"Bon," nodded the frenchman.

"So, I'm offering you four drawings by Ernst plus one sketch by Magritte, and in return you give me three sketches by Magritte and two paintings by Bacon. It's perfectly fair, isn't it?"

Blanchard remained silent, he had the feeling that something was wrong.

Was the Italian dealer offering a fair swap?

### Swapping Art Puzzle Solution

The swap is unfair. If we abbreviate with an E the drawings by Ernst, an M for Magritte's sketches, and a B for Bacon's paintings, we can rewrite the equations as stated by the Italian dealer as:
1. EEEE = MMMMM (both dealers agreed on this)
2. MME = BB (again, both dealers agreed on this too)
3. MMMBB = EEEEM (the French dealer wasn't sure of this)
Now, if for the 3rd equation we substitute BB with MME (from equation 2), we'll have a 4th equation: MMMMME = EEEEM. But the 1st equation states that MMMMM = EEEE, so it is possible to cancel out, in equation 4, MMMMM on the left and EEEE on the right. This would leave us with the equation E = M, which does not fit with equation 1, where E is obviously greater than M.

The problem gives us 3 equations:
1. 4x = 5y
2. 2y + x = 2z
3. 3y + 2z = 4x + y

Equation 2. can be rewritten as:
4. x = -2y + 2z

Equation 3. can be rewritten as:
5. 4x = 2y + 2z

Adding equations 4. and 5. gives us:
6. 5x = 4z

Combining 1. and 6., we get:
7. 4x = 5y = (16/5)z

If we convert the offer (3.) in terms of y, we get:
8. 3y + 2(25/16)y = 5y + y
ie 3y + (25/8)y = 6y
ie 6.125y = 6y

The last equation is not absolutely true, which proves the swap is unfair.