8
Part of 1996 All-Russian Olympiad
Problems(3)
$5\times 7$ covered by triomino
Source: All-Russian Olympiad, Grade 9, Second Day, Problem 8
4/18/2013
Can a checkerboard be covered by L's (figures formed from a square by removing one of its four corners), not crossing its borders, in several layers so that each square of the board is covered by the same number of L's?M. Evdokimov
combinatoricscheckerboard
Ten $x^2 +px+q$
Source: All-Russian Olympiad 1996, Grade 10, Second Day, Problem 8
4/18/2013
Goodnik writes 10 numbers on the board, then Nogoodnik writes 10 more numbers, all 20 of the numbers being positive and distinct. Can Goodnik choose his 10 numbers so that no matter what Nogoodnik writes, he can form 10 quadratic trinomials of the form , whose coeficients and run through all of the numbers written, such that the real roots of these trinomials comprise exactly 11 values?I. Rubanov
quadraticsalgebra proposedalgebra
How find the order of all numbers?
Source: All-Russian Olympiad 1996, Grade 11, Second Day, Problem 8
4/19/2013
The numbers from 1 to 100 are written in an unknown order. One may ask about any 50 numbers and find out their relative order. What is the fewest questions needed to find the order of all 100 numbers?S. Tokarev
combinatorics proposedcombinatorics