An investigation is being conducted into the case of a stolen mustang. There are three suspects – Bill, Joe and Sam. At the trial, Sam said that the mustang was stolen by Joe. Bill and Joe also testified, but what they said, no one remembered, and all the records were lost. In the course of the trial it became clear that only one of the defendants had stolen the Mustang, and that only he had given a truthful testimony. So who stole the mustang?
On an island, there are knights who always tell the truth, and liars who always lie. What question would you need to ask the islander to find out if he has a crocodile at home?
15 points are placed inside a $4 \times 4$ square. Prove that it is possible to cut a unit square out of the $4 \times 4$ square that does not contain any points.
In a purse, there are 2 coins which make a total of 15 pence. One of them is not a five pence coin. What kind of coins are these?
In the language of the Ancient Tribe, the alphabet consists of only two letters: M and O. Two words are synonyms, if one can be obtained by from the other by a$)$ the deletion of the letters MO or OOMM, b$)$ adding in any place the letter combination of OM. Are the words OMM and MOO synonyms in the language of the Ancient Tribe?
One person says: “I’m a liar.” Is he a native of the island of knights and liars?
In a race between 6 athletes, Andrew falls behind Boris and two athletes finish between them. Vincent finished after Declan, but before George. Declan finished before Boris but after Eric. Which order did the athletes finish the race in?
Are the sum and product odd or even for:
a$)$ two even numbers?
b$)$ two odd numbers?
c$)$ an odd and an even number?
1.A bagel is cut into sectors. Ten cuts were made. How many pieces did this make?
2. Woodchucks are sawing a log. They made 10 cuts. How many pieces were made?
How can we explain why the answers in the previous two questions are different?
A bagel is cut into sectors. Ten cuts were made. How many pieces did this make?
Jemima always tells the truth, but when she was asked the same question twice, she gave different answers. What kind of question could this be?
Fred always tells the truth, but Vadim always lies. What question should they be asked, so that they would give the same answers?
The tower clock chimes three times in 12 seconds. How long will six chimes last?
Seven nines written out in a series: 9 9 9 9 9 9 9. Put some “+” or “-” between some of them, so that the resultant expression equals 1989.
This problem is from Ancient Rome.
$\\$ A rich senator died, leaving his wife pregnant. After the senator’s death it was found out that he left a property of 210 talents (an Ancient Roman currency) in his will as follows: “In the case of the birth of a son, give the boy two thirds of my property (i.e. 140 talents) and the other third (i.e. 70 talents) to the mother. In the case of the birth of a daughter, give the girl one third of my property (i.e. 70 talents) and the other two thirds (i.e. 140 talents) to the mother.”
$\\$ The senator’s widow gave birth to twins: one boy and one girl. This possibility was not foreseen by the late senator. How can the property be divided between three inheritors so that it is as close as possible to the instructions of the will?
Everyone believed that the Dragon was one-eyed, two-eared, three-legged, four-nosed and five-headed. In fact, only four of these definitions form a certain pattern, and one is redundant. Which characteristic is unnecessary?
Decipher the numerical puzzle system
$MA \times MA = MIR$
$AM \times AM = RIM$
$($different letters correspond to different numbers, and identical letters correspond to the same numbers$)$.
Restore the numbers. Restore the digits in the following example by dividing as is shown in the image
Burbot-Liman. Find the numbers that, when substituted for letters instead of the letters in the expression $NALIM × 4 = LIMAN,$ fulfill the given equality (different letters correspond to different numbers, but identical letters correspond to identical numbers)