9.1

Part of I Soros Olympiad 1994-95 (Rus + Ukr)

Problems(3)

2 sets from {3, 4, 5, ...,13, 14} (I Soros Olympiad 1994-95 R1 9.1 10.1)

Source:

Divide the set of twelve numbers

A = \{3, 4, 5, ...,13, 14\}

B

C

'of six numbers each according to this condition: for any two different numbers with

B

their sum does not belong to

B

and for any two different numbers from

C

, the sum does not belong to

C

combinatoricsSubsets

ab and cd divides abcd (I Soros Olympiad 1994-95 R2 9.1)

Source:

1995

is divisible by both

19

95

. How many four-digit numbers are there that are divisible by two-digit numbers formed by both its first two digits and its last two digits?

wonderful , hour and minutes, clock (I Soros Olympiad 1994-95 Ukraine R2 9.1)

Source:

Let's call this position of the hour and minute hands on the analog clock wonderful, during which the hands change places after some time. Count the total number of wonderful clockwise positions.

algebrageometry