9.5

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(3)

numbers 0-2 in nxn board (IV Soros Olympiad 1997-98 Correspondence 9.5)

Source:

There is a square table with side

n

. Is it possible to enter the numbers

0

1

2

into the cells of this table so that all sums of numbers in rows and columns are different and take values from

1

2n

n = 7

n = 8

locus of center of rotations

Source: V Soros Olympiad 1997-98 R3 9.5 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

ABC

. Find the locus of points

M

such that there is a rotation with center at

M

C

to a certain point on side

AB

geometryrotationLocusgeometric transformation

...<5/8< ... (IV Soros Olympiad 1997-98 R2 9.5)

Source:

All ordinary proper irreducible fractions whose numerators are two-digit numbers were ordered in ascending order. Between what two consecutive fractions is the number

\frac58

algebrainequalities