MathDB

Palindromic Numbers

Source: Romanian District Olympiad 2014, Grade 5, P2

June 15, 2014

floor functionnumber theory proposednumber theory

Problem Statement

Let

M

be the set of palindromic integers of the form

5n+4

where

n\ge 0

is an integer.
[*]If we write the elements of

M

in increasing order, what is the

50^{\text{th}}

number? [*]Among all numbers in

M

with nonzero digits which sum up to

2014

which is the largest and smallest one?