3
Part of 1999 May Olympiad
Problems(2)
numbers on a 3x10 board
Source: V May Olympiad (Olimpiada de Mayo) 1999 L2 P3
9/17/2022
The first row of this table is filled with the numbers through , in that order.
The second row is filled with the numbers from to , in any order.
In each box of the third row the sum of the two numbers written above is written.
Is there a way to fill in the second row so that the ones digits of the numbers in the third row are all different?
https://cdn.artofproblemsolving.com/attachments/8/5/41117d105cc880bf452fa46132c20f2167aa5b.png
combinatorics
on each step of a ladder with 10 steps there is a frog
Source: V May Olympiad (Olimpiada de Mayo) 1999 L1 P3
9/17/2022
On each step of a ladder with steps there is a frog. Each of them can, in one jump, be placed on another step, but when it does, at the same time, another frog will jump the same number of steps in the opposite direction: one goes up and another goes down. Will the frogs manage to get all together on the same step?
algebracombinatorics