1

Part of 2018 May Olympiad

Problems(2)

4-digit perfect squares May Olympiad (Olimpiada de Mayo) 2018 L2 P1

Source:

4

-digit whole number that is a perfect square. Another number is built adding

1

to the unit's digit, subtracting

1

from the ten's digit, adding

1

to the hundred's digit and subtracting

1

from the ones digit of one thousand. If the number you get is also a perfect square, find the original number. It's unique?

number theoryDigitsPerfect SquaresPerfect Square

a list of 2018 numbers , max last no 2018 May Olympiad L1 p1

Source:

Juan makes a list of

2018

numbers. The first is

1

. Then each number is obtained by adding to the previous number, one of the numbers

1

2

3

4

5

6

7

8

9

. Knowing that none of the numbers in the list ends in

0

, what is the largest value you can have the last number on the list?