1

Part of 2001 May Olympiad

Problems(2)

broken key on calculator

Source: VII May Olympiad (Olimpiada de Mayo) 2001 L2 P1

In my calculator, one of the keys from

1

9

does not work properly: when you press it, a digit between

1

9

appears on the screen that is not the correct one. When I tried to write the number

987654321

, a number divisible by

11

appeared on the screen and leaves a remainder of

3

when divided by

9

. What is the broken key? What is the number that appeared on the screen?

digits' problem, last digit 2

Source: VII May Olympiad (Olimpiada de Mayo) 2001 L1 P1

Sara wrote on the board an integer with less than thirty digits and ending in

2

. Celia erases the

2

from the end and writes it at the beginning. The number that remains written is equal to twice the number that Sara had written. What number did Sara write?

number theoryDigits