Mirrors

Why do mirrors flip left and right but do not flip up and down?

Solution coming soon.

No Body, No Nose

What do you call a person with no body and no nose?

The answer is NOBODY KNOWS (no-body-nose).

The Connect Game

Two friends are playing the following game:

They start with 10 nodes on a sheet of paper and, taking turns, connect any two of them which are not already connected with an edge. The first player to make the resulting graph connected loses.

Who will win the game?

Remark: A graph is “connected” if there is a path between any two of its nodes.

The first player has a winning strategy.

His strategy is with each turn to keep the graph connected, until a single connected component of 6 or 7 nodes is reached. Then, his goal is to make sure the graph ends up with either connected components of 8 and 2 nodes (8-2 split), or connected components of 6 and 4 nodes (6-4 split). In both cases, the two players will have to keep connecting nodes within these components, until one of them is forced to make the graph connected. Since the number of edges in the components is either C^8_2+C^2_2=29, or C^6_2+C^4_2=21, which are both odd numbers, Player 1 will be the winner.

Once a single connected component of 6 or 7 nodes is reached, there are multiple possibilities:

1. The connected component has 7 nodes and Player 2 connects it to one of the three remaining nodes. Then, Player 1 should connect the remaining two nodes with each other and get an 8-2 split.
2. The connected component has 7 nodes and Player 2 connects two of the three remaining nodes with each other. Then, Player 1 should connect the large connected component to the last remaining node and get an 8-2 split.
3. The connected component has 7 nodes and Player 2 makes a connection within it. Then, Player 1 also must connect two nodes within the component. Since the number of edges in a complete graph with seven nodes is C^7_2=21, eventually Player 2 will be forced to make a move of type 1 or 2.
4. The connected component has 6 nodes and Player 2 connects it to one of the four remaining nodes. Then, Player 1 should make a connection within the connected seven nodes and reduce the game to cases 1 to 3 above.
5. The connected component has 6 nodes and Player 2 connects two of the four remaining nodes. Then, Player 1 should connect the two remaining nodes with each other. The game is reduced to a 6-2-2 split which eventually will turn into either an 8-2 split, or a 6-4 split. In both cases Player 1 will win, as explained above.

Seven Letters Sequence

Find a seven-letter sequence to fill in each of the three empty spaces and form a meaningful sentence.

The ★★★★★★ surgeon was ★★ ★★★ to operate, because there was ★★★★.

The sequence is NOTABLE:

The NOTABLE surgeon was NOT ABLE to operate, because there was NO TABLE.

Glow and Shine

There is a property that applies to all words in the first list and to none in the words in the second list. What is it?

• GLOW, ALMOST, BIOPSY, GHOST, EMPTY, BEGIN
• SHINE, BARELY, VIVISECTION, APPARITION, VACANT, START

The words in the first list are called “Abecederian”, i.e. their letters are in alphabetical order.

Escaping the Kingdom

A long time ago there was a kingdom, isolated from the world. There was only one way to and from the kingdom, namely through a long bridge. The king ordered the execution of anyone caught fleeing the kingdom on the bridge and the banishment of anyone caught sneaking into the kingdom.

The bridge was guarded by one person, who was taking a 10-minute break inside his cabin every round hour. Fifteen minutes were needed for a person to cross the bridge and yet, one woman managed to escape the kingdom. How did she do it?

Once the guard entered the cabin, the woman started crossing the bridge for 9 minutes, and then turned around and pretended to be going in the opposite direction for one more minute. When the guard caught her, she said she was trying to enter the kingdom, so he banished her away.

Unconscious and Bleeding

A man is found unconscious in front of a store at two in the morning. His head is bleeding and there is a brick laying next to him. When the police arrive, they carry the man to jail. Why did they arrest him?

The man was a burglar who tried to break the store’s glass with the brick. The glass turned out to be bullet proof, so the brick bounced back and hit him in the head, knocking him out.

Pretty Words

Can you recognize the four words below?

• ZO-ZO
• ZOOZ
• OON
• ZCZ

If you rotate the screen by 90°, you will read vertically:

• ONION
• NOON
• ZOO
• NUN