The document contains 10 puzzles with their solutions. Puzzle 1 involves figuring out a password system by observing people entering a building. Puzzle 2 is about calculating how many people can escape a spaceship before it explodes based on trip times and capacity. Puzzle 3 asks how to determine which of 7 metal bars is gold using a balance scale in the minimum number of weighings.

1. 10 Puzzles
with Solutions
by Fabrizio Valerio Covone

2. Puzzle 1
A spy wants to enter in a top secret building, but the guard at the
entrance asks everyone a password.
For this reason the spy hides out and wait for someone, so he can
have a peek. A person comes and the guard says:
“Wait! If I say six which is the password?”
“Three!”
“Ok, come in.”
The spy thinks: “mmh… I guess how it works…” But to be sure he
keeps hiding and wait for another person. Another one comes:
“Hold on! If I say twelve which is the password?”
“It’s six!”
“Ok, come in.”
“Ok I got it” the spy thinks and try enter, but obviously is stopped by
the guard asking the password:
“Hey you, wait! if I say eight which is the password?”
“I bet it’s four!”
The guard in second takes his gun and shoots down the spy.
Which was the right answer?

3. Puzzle 1
The right answer is five!
Because the guard wants to know the
exact amount of letters of the number
he says instead of the division by 2.

4. Puzzle 2
A spaceship has a failure and auto-destruction activates itself. The 20 people crew
have exactly 13 minuets to escape from such a deadly trap.
But the safety escape pod is capable to carry a total of 4 people and there aren’t any
space suites. Furthermore, a trip to the nearest planet and back takes 3 minutes.
How many people will survive?

5. Puzzle 2
There is enough time for 5 trips before the spaceship blows, but
since starting from the 2nd trip one place is taken by the pilot.
4 + 3 + 3 + 3 + 3 = 16
So, only 16 crew members will survive.

6. Puzzle 3
An explorer finds a secret chamber in a pyramid. Inside the chamber there are 7
identical metal bars and a rusty 2 scale pans balance.
An inscription on the wall says that only 1 of the metal bars is made of gold the other
ones are made of pyrite (a metal similar to gold but slightly heavier and worthless).
The explorer wants to take only the gold bar, but he is very lazy and wants to figure it
out doing as less weightings as possible.
Which is the minimum number of weightings?

7. Puzzle 3
The right answer is 2.
During the 1st weighting the explorer will put 3 metal bars on each scale pan.
If the pans are balanced then the gold bar is the one not on the pans.
Otherwise, the explorer will take the lighter 3 bars group and puts one metal
bar on each scale pan.
Following a similar procedure, if the pans are balanced then the gold bar is
the one not on the pans.
Otherwise the lighter one is the golden bar.

8. Puzzle 4
A, B, C and D are single-digit numbers.
The following equations can all be made with these numbers.
Find the values of each digit.
A+B=D
B−A=C
2×C=8
D÷3=2

9. Puzzle 4
The right answer is:
A=1
B=5
C=4
D=6
As a matter of fact the equations with correct values are:
1+5=6
5−1=4
2×4=8
6÷3=2

10. Puzzle 5
Have a look at this wonderful example of modern art.
How many squares can you see?
Be sure to count overlapping squares separately.

11. Puzzle 5
The right answer is 22.

12. Puzzle 6
Only one of these pictures can be drawn with one line without lifting your
pen from the paper or retracting any lines.
Which one is it?

13. Puzzle 6
The right answer is B.

14. Puzzle 7
During lesson break someone ate all classroom snacks, interrogated by the
teacher the 3 students in the classroom gave the following statement:
A:“C is lying, I saw him eating the snacks.”
B: “I didn’t see anything.”
C: “B is a liar, I saw him taking the snacks from the bags. ”
Only one of them is saying the truth. So, who ate the snacks?
A B C

15. Puzzle 7
B is the snack thief, because only C is telling the truth.
A B C

16. Puzzle 8
Three of the four shapes below can be combined to form a square. Which one
isn’t used?
Feel free to rotate the shapes.
A B
C
D

17. Puzzle 8
The right answer is A. Below you can see the square as a result of B, C and D
combination.
B C
D

18. Puzzle 9
Joe forgot his wedding anniversary,
but thanks to his brand new
smartphone he got a reminder just
1 hour before his wife’s alarm rings.
Now he has to buy a present at the A
jewelry, to take the breakfast at the B
restaurant and to rent her favorite
movie before she wakes up.
C
For this reason he has to to do the
shortest travel possible. Be careful,
only grey roads at the borders are
two-way. While blue roads are one-
way following arrows direction.
Which is the shortest trip D
sequence?

19. Puzzle 9
The shortest trip sequence is:
A -> C -> D -> B -> A
Look at the image to the right for
A
path details. B
C
D

20. Puzzle 10
On a tree there is a nest with ten eggs. On winter time a strong wind gust
shook the nest and two eggs fell down. Furthermore during an heavy spring
rain, a cracked branch fell and cracked three eggs.
Assuming that no other accidents happen, how many eggs are left at the end
of the summer?

21. Puzzle 10
The right answer is 0. Because during the summer the five remaining eggs will
hatch.