MathDB

4

Part of 2021 Durer Math Competition Finals

Problems(2)

mystical sequences x_{i+1} = [ x_i ] {x_i}

Source: 2021 Dürer Math Competition Finals Day 1 E4 E+2

1/2/2022
Indians find those sequences of non-negative real numbers x0,x1,...x_0, x_1,... mystical t hat satisfy x0<2021x_0 < 2021, xi+1=⌊xi⌋{xi}x_{i+1} = \lfloor x_i \rfloor \{x_i\} for every i≥0i \ge 0, furthermore the sequence contains an integer different from 00. How many sequences are mystical according to the Indians?
floor functionSequencealgebra
4-digit numbers that contains exactly 3 different digits

Source: 2021 D&uuml;rer Math Competition Finals Day2 E4 https://artofproblemsolving.com/community/c2749870_

1/8/2022
What is the number of 44-digit numbers that contains exactly 33 different digits that have consecutive value? Such numbers are for instance 54645464 or 20012001.
Two digits in base 1010 are consecutive if their difference is 11.
Digitsnumber theory