## Death Cult

A thousand people stand in a circle in order from 1 to 1000. Number 1 has a sword. He kills the next person (Number 2) and gives the sword to the next living person (Number 3). All people keep doing the same until only one person remains. Which number survives?

First, we note that if the number of people is a power of 2, then the first person will survive every round. The greatest power of 2 that is less than 1000 is 512. Therefore, after 488 people die, there will be 512 remaining and the first one to kill the 489-th person will survive. This person has number 1+2×488=977.

## A String Around a Rod

A string is wound around a circular rod with circumference 10 cm and length 30 cm. If the string goes around the rod exactly 4 times, what is its length?

Imagine the circular rod is actually a paper roll and the string is embedded inside the paper. When we unroll it, we get a paper rectangle 30cm×40cm with the string embedded along the diagonal. Using the Pythagorean theorem, we find that the length of the string is 50cm.

## A Heart That Doesn’t Beat

I have a heart that doesn’t beat.
I have a mouth that doesn’t speak.
I have a head that doesn’t think.

What am I?

The answer is ARTICHOKE.

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## Imprisoned Logicians

Two friends, logicians – Ein and Stein – get imprisoned in two distant cells in a castle. Both cells have just one door, and a window with 8 bars in the first cell, and 12 bars in the second cell. The first day both logicians get the same letter from the prison master:

“The total number of bars in the two prison cells in this castle is either 18 or 20. Starting tomorrow, every morning I will go first to Ein and then to Stein, and will ask how many bars the other logician has. If one of you answers correctly, I will immediately let both of you leave the castle. If one of you answers incorrectly, I will execute both of you. Of course, you can always decide not to answer and just stay imprisoned.
I have sent a copy of this letter to you and your friend. There is no point in trying to communicate with him – your cells are far away from each other, and he won’t hear you.”

Will the logicians manage to escape the castle eventually? When will they do it?

Solution coming soon.

## Get One Hundred

9 8 7 6 5 4 3 2 1 = 1 0 0

Add +, +, +, – anywhere above in order to get a valid equality.

9 8-7 6+5 4+3+2 1 = 1 0 0

## Black-White Maze

Find your way through this black-white maze, created by William Leonard.

The solution is shown below.

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## Lost In the Forest

You are lost in the middle of a forest, and you know there is a straight road exactly 1 km away from you, but not in which direction. Can you find a path of distance less than 640 m which will guarantee you to find the road?

Imagine there is a circle with a radius of 100 m around you, and you are at its center O. Let the tangent to the circle directly ahead of you be t. Then, follow the path:

1. Turn left 30 degrees and keep walking until you reach the tangent t at point A for a total of 100×2√3/3 meters, which is less than 115.5 meters.
2. Turn left 120 degrees and keep walking along the tangent to the circle until you reach the circle at point B for a total of 100×√3/3 which is less than 58 meters.
3. Keep walking around the circle along an arc of 210 degrees until you reach point C for a total of 100×7π/6 which is less than 366.5 meters.
4. Keep walking straight for 100 meters until you reach point D on the tangent t.

## An Ant’s Path

An ant is positioned at one of the vertices of a cube and wants to get to the opposite vertex. If the edges of the die have length 1, what is the shortest distance the ant needs to travel?

We unfold a cube to get a cross-shaped figure. Then, the problem is to find the shortest path between two points separated by a horizontal distance of 2 units and a vertical distance of 1 unit.

It is easy to see that the path in question is the one passing through the middle of the edge between the start and end points, and which has a distance of √5.

## Dr. Riesen’s Rebuses 1

Can you figure out what these love-related expressions these rebuses represent?

1. Be mine
2. Love at first sight
3. True love forever
4. Love is in the air
5. Romance
6. Sweet nothings
7. XOXO
8. Written in the stars
9. Sweetheart
10. Love birds
11. Heart throb
12. Pucker up
13. Love is love
14. You complete me
15. Lover’s gaze
16. Love struck
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## Kings and Queens

What should follow the sequence of diagrams shown below?

The diagrams represent consecutive monarchs of England:

1. King Edward the 8-th → Ke8
2. King George 6-th → Kg6
3. Queen Elizabeth 2-nd → Qe2

Therefore, the next diagram should represent King Charles the 3-rd → Kc3.