# Logical riddles

When I was around 20 I created these riddles as a birthday present for a friend of mine. Some of them are inspired by Zweisteins "Logeleien" for the Newspaper "ZEIT".

Now I thought that this work is too nice to hide in a box. Have fun!

## 1. Labyrinth

Find a way from the center to the outside.

## 2. Hexagon walk

Walk across the hexagon such that the sum of all numbers you pass is 16. The numbers must be passed in ascending order. You must not use any path a second time. Your way must begin and end outside the hexagon.

## 3. The election

In my home town, just like every four years, a city council election took place. It was, of course, an extremely important event for the community. So it was quite clear that the local newspaper dealt with it. A week before the election it polled some citizens, which of the eight candidates will be elected in their opinion.

These are the predictions of 16 citizens:

- Franklin and Harrison will not be elected.
- Adams makes it to the city council, Baker and Edwards won't.
- Adams and Baker will certainly not be elected but Dickinson and Franklin will.
- Except Baker, Carter and Dickinson all others will make it to the city council.
- Carter and Edwards will be elected, Baker won't.
- Neither Adams nor Carter will be elected.
- Edwards and Dickinson won't be elected while Harrison will make it to the city council.
- Dickinson and Gardiner have no chance, but Adams will be chosen.
- We'll see Baker and Gardiner in the city council.
- Franklin will make it Dickinson and Edwards won't.
- Carter and Hameier lose the election while Edwards and Franklin are among the winners.
- Gardiner will be elected, Adams and Franklin not.
- Dickinson will be in the city council, not Carter.
- Baker, Carter and Harrison will be elected.
- It is quite certain that Gardiner and Harrison will not be elected.
- Carter and Dickinson will be elected, Edwards and Gardiner won't make it.

The election passed and it turned out that not one of the 16 forecasts was completely correct. This will enable you to find out which of the eight candidates made the leap into the city council. Who?

## 4. A point of view

These are four views from a labyrinth based on a 4 x 4 grid. You can reconstruct the complete labyrinth. What does the top view look like?

## 5. Slices

A 3 x 3 x 3 cube is build of 27 small black or white cubes. In one specific cube you'll find the slices A, B, C and D. Of course they could be rotated in any way. Only one of the slices 1, 2, 3 or 4 could also been found in the cube. Which one?

## 6. Statements

Which of the following statements are true and which are false?

- The statements 3, 4 and 7 are false.
- The statements 1 and 7 are true.
- The statements 2, 4 and 6 are false.
- The statements 2 and 8 are false.
- The statements 6 and 8 are true.
- The statements 1, 2 and 3 are false.
- The statements 5 and 8 are false.
- The statements 3 and 7 are true.

## 7. Crossing checksums

The numbers below are sums to fill the grid with. For example: horizontal A-22 means, the five digits of the number in the first row starting from A has to sum up to 22. There are some limitations: The digits of a number all has to be different. And the number must not start or end with zero.

```
Horizontal Vertical
A-22 L-21 R-14 A-10 F-19 Q-18
F-11 M-11 S-25 B-20 G-18 T-6
H-4 N-3 U-8 C-11 K-12 V-16
I-20 O-9 W-8 D-27 M-13
J-6 P-7 X-20 E-10 O-8
```

## 8. Broken flashlight

I had to drive to the city some days ago but noticed that the left flashlight at my car was broken. Still, I took the car but avoided to turn left at any corner. Coming back home I remembered that I didn't drive any street more than once except some crossings that I passed twice. But I didn't turn right at those crossings. I also remembered that I passed all the red marks.

There is only one way that matches all those conditions. What was my way through the city?

## 9. A sequence of letters

Which letter should be at the place of the question mark?

W, L, S, B, A, T, P, O, T, ?

## 10. Murder in Knusiland

Some time ago I got mail from Knusiland. Everybody knows that there are three tribes in Knusiland. The Abians are telling the truth all the time. The Bebians are always lying and the Cebians tell the truth and lie alternately.

This time, the local police inspector – who of course is an Abian – asked me for help. He wrote that a murder happened and that there are three suspects from whom exactly one must be the murderer. Their names are Lollinger, Momminger and Nonninger. The inspector also knew that one of those is an Abian, one is a Bebian and the third a Cebian. But not which man is which. The suspects knew though, who is from which tribe.

The inspector gave me the transcript of an interview with the suspects:

- Lollinger: I didn't commit the murder.
- Momminger: I am the murderer.
- Nonninger: Both statements just given are wrong.
- Lollinger: From the three statements just given, exactly one is true.
- Momminger: From the four statements just given, there are more wrong than true.
- Nonninger: I never lie.

Who is the murderer?

## 11. Round trip

Search for a way through the maze that passes all numbers in the order 1-2-3-1-2-3-1-2-3. No path must be used more than once. End your trip at the place you've started.

## 12. A Calculation

In the following calculation replace any letter and star by a digit (0 – 9) to get a correct multiplication. Same letters are the same digit, different letters are different digits. A star could be replaced by any digit.

```
P F E I L • T E L L
-------------------
* * * * *
* * * * *
A P F E L
A P F E L
-------------------
* * * * * T * *
```

Which letter is which number?

## 13. Crossing numbers

Fill in numbers to match all conditions. Put a digit (1 – 9) in every cell. Don't use zeros.

#### Horizontal

A – Same digits as C-vertical

F – Factor of A-horizontal

H – Square root of C-vertical

I – Multiple of G-vertical

K – Multiple of N-vertical

M – Cubic number

O – Palindrome^{*}

Q – Prime number

R – Cubic number

#### Vertical

A – Q-horizontal and R-horizontal multiplied

B – Square number

C – Every digit is greater than the previous

D – Every digit is divisible by 3, the whole number is divisible by 9

E – Multiple of P-vertical

G – Multiple of J-vertical

J – Prime number

L – Prime number

N – Square number

P – Palindrome^{*}

^{*}Palindrome: a number which reads the same backward as forward.