Enigmas

A mouse found itself in the middle of a perfectly circular swimming pool while trying to escape a cat. She knows that she swims three times slower than the cat runs, but the cat won't enter the water and if she doesn't get caught coming out of the water she will manage to escape.

Can the mouse run away?

The Strasbourg architect wants to build the second spire of the Cathedral of Strasbourg. However, shortly after construction began, sabotage took place. One of the 14 huge stones which arrived yesterday on the site were replaced by a stone of the same shape but of poor quality that does not weigh the same as good quality stones, but we don't know if it is heavier or lighter. On the construction site, there is a huge scale with two platforms which allows you to compare the weight of stones. It is so big that it takes a whole day to do a single weighing. A worker warns him that there is still a stone that he knows to be of good quality, but it must be used tomorrow.

Can the architect find the poor quality stone in 3 days?

(Thanks to Paul Laubie for this one)

During her exploration of an ancient maze, Celica arrives in a room where there are four chests with inscriptions on them. She knows that only one chest contains treasure, the other three are trapped. She also knows that two of the inscriptions are true and two are false.

A: I'm telling the truth!

B: A is lying. C too.

C: The treasure is in a lying chest.

D: If this setence were on A, it would say that the treasure is in B.

Where is the treasure?

Shortly after finding her first treasure, Celica ends up arriving in a room where there are four more chests with inscriptions on them. She knows that only one chest contains treasure, the other three are trapped. She also knows that some inscriptions are true and others are false.

A: My hinges are gold.

B: A or D is lying, or both. C tells the truth.

C: Between A and D, only one lie.

D: The treasure is in a lying chest.

After some time thinking, she opens one of the four chests and finds the treasure.

Which chest did she open?

Tressa, an experienced merchant, has some problems with her cylindrical containers: she only finds those of 1L, 2L, 5L and 10L. The problem is that she must be able to serve her goods per 0.5L to satisfy all its customers.

How can she get 0.5L?

A sailing boat sails in clear weather on a calm sea at 7 km/h. After a moment, in the crow's nest, the lookout shouts when he sees the flame of the lighthouse of the city to which they are going to. He knows that when he manages to see it, they only have 50 km left before arriving. Precisely three hours later, a sailor working on the surface of the water finally sees the light of the lighthouse appear on the horizon. 

How tall is the lighthouse? 

(Reminder: the earth's radius is 6371 km.)

Shulk has to open a five-digit padlock, but all he knows is that the code is a very special number: it's double one number, triple another number, the square of yet another number and the cube of yet another number.

What is the code?

Lin has just developed a material whose robustness she wants to test. To do this, she makes two balls from this material that are identical in every way; she cannot do more due to the scarcity of raw materials. She will then go to a 100-story building, place herself on a well-chosen floor and release one of her two balls. Her goal is to determine the first floor at which the ball will break when hitting the ground. She could do all the floors one by one starting from the first until she finds the first one where the ball will break, but in this case she risks having to do 100 tests.

How can she minimize the number of tests to be done?

Izana is organizing a party at his house and has a brilliant idea: He arranges a hundred lamps to which he associates a label with a number from 1 to 100 and he asks each of his guests as soon as they arrive to activate all the buttons of the lamps whose number is a multiple of its order of arrival. For example, the first to arrive lights all the lamps. The second turns off all even lamps. The third will turn off lamp 3, turn on 6, turn off 9, etc.

Once the hundred guests have arrived, which lamps are lit?

On the Xth day of the Yth month of the Zth year of the 20th century a ship was wrecked. It had U smokestacks, V propellers and W crew members. If we do the product XYZUVW to which we add the cubic root of the captain's age we obtain 4,002,331.

How old is the captain?

(Note: we assume that U, V, W, X, Y and Z are different from 1)

Old Bernard lives as a hermit in the depths of a forest and the inhabitants of the neighboring village ask many questions about his exact date of birth. Here is the information they were able to find:

• Bernard was born between 1900 and 1999.

• The last digit of his year of birth is odd.

• He was born during the winter, between November and February.

• He was born on a Thursday.

• His day of birth is in the second half of the month.

• His month of birth has 31 days.

• You must multiply his month of birth by 2 to find his day of birth.

• He is over 95 years old.

• December 31, 1900 was a Monday.

When was Bernard born?

(Reminder: we are in 2018 here.)