Find out the principles by which the numbers are depicted in the tables (shown in the figures below) and insert the missing number into the first table, and remove the extra number from the second table.
The Olympic gold-medalist Greyson, the silver-medalist Blackburn and bronze-medalist Reddick met in the club before training. “Pay attention,” remarked the black-haired one, “one of us is grey-haired, the other is red-haired, the third is black-haired. But none of us have the same colour hair as in our surnames. Funny, is not it?”. “You’re right,” the gold-medalist confirmed. What color is the hair of the silver-medalist?
A square piece of paper is cut into 6 pieces, each of which is a convex polygon. 5 of the pieces are lost, leaving only one piece in the form of a regular octagon (see the drawing). Is it possible to reconstruct the original square using just this information?
Try to get one billion \(1000000000\) by multiplying two whole numbers, in each of which there cannot be a single zero.
Ten people wanted to found a club. To do this, they need to collect a certain amount of entrance fees. If the organizers were five people more, then each of them would have to pay £100 less. How much money did each one pay?
Teams A, B, C, D and E participated in a relay. Before the competition, five fans expressed the following forecasts.
1) team E will take 1st place, team C – 2nd;
2) team A will take 2nd place, D – 4th;
3) C – 3rd place, E – 5th;
4) C – 1st place, D – 4th;
5) A – 2nd place, C – 3rd.
In each forecast, one part was confirmed, and the other was not. What place did each team take?
In the race of six athletes, Andrew lagged behind Brian and two more athletes. Victor finished after Dennis, but before George. Dennis beat Brian, but still came after Eustace. What place did each athlete take?
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).