MathDB

1

Part of 1995 All-Russian Olympiad

Problems(2)

hours and minutes

Source: All-Russian olympiad 1995, Grade 9, First Day, Problem 1

10/20/2013
A freight train departed from Moscow at xx hours and yy minutes and arrived at Saratov at yy hours and zz minutes. The length of its trip was zz hours and xx minutes. Find all possible values of xx.
S. Tokarev
algebra proposedalgebra
the numbers 1...100 be covered with 12 geom progressions

Source: All-Russian olympiad 1995, Grade 11, First Day, Problem 1

10/21/2013
Can the numbers 1,2,3,…,1001,2,3,\ldots,100 be covered with 1212 geometric progressions?
A. Golovanov
inequalitiesgeometric sequencenumber theory proposednumber theory