Decipher the numerical puzzle system \[\left\{\begin{aligned} & MA \times MA = MIR \\ & AM \times AM = RIM \end{aligned}\right.\] (different letters correspond to different numbers, and identical letters correspond to the same numbers).
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?
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?
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.
The tower clock chimes three times in 12 seconds. How long will six chimes last?
Fred always tells the truth, but George always lies. What question could you ask them so that they would give the same answer?
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?
Woodchucks are sawing a log. They made 10 cuts. How many pieces were made?
A bagel is cut into sectors. Ten cuts were made. How many pieces did this make?
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?