MathDB

3

Part of 1979 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1979 Problem 1.3

Source: Bundeswettbewerb Mathematik 1979 Round 1

9/23/2022
In base 1010 there exist two-digit natural numbers that can be factorized into two natural factors such that the two digits and the two factors form a sequence of four consecutive integers (for example, 12=3⋅412 = 3 \cdot 4). Determine all such numbers in all bases.
other basesnumber theoryconsecutiveBases
Bundeswettbwerb Mathematik 1979 Problem 2.3

Source: Bundeswettbewerb Mathematik 1979 Round 2

9/23/2022
The nn participants of a tournament are numbered with 00 through n−1n - 1. At the end of the tournament it turned out that for every team, numbered with ss and having tt points, there are exactly tt teams having ss points each. Determine all possibilities for the final score list.
combinatoricspoints