Replace the letters in the word \(TRANSPORTIROVKA\) by numbers (different letters correspond to different numbers, but the same letters correspond to identical numbers) so that the inequality \(T > R > A > N < P <O < R < T > I > R > O < V < K < A\).
Restore the numbers. Restore the digits in the following example by dividing as is shown in the image
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?
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?
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?
Are the sum and product odd or even for:
a) two even numbers?
b) two odd numbers?
c) an odd and an even number?
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?
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.