A four-digit number can be made by repeating a two-digit number. For example, 1111 is made by repeating 11, and 1919 is made by repeating 19. How many such numbers are there between 2000 and 10 000?
, 2020
Pick one
Solution
Each four-digit number must be greater than 2000, and so the smallest two-digit number that may be repeated is 20 (to give 2020).
Each four-digit number must be less than 10 000, and so the largest two-digit number that may be repeated is 99 (to give 9999).
Each two-digit number between 20 and 99 may be repeated to give a four-digit number between 2000 and 10 000.
In total, there are numbers that satisfy the given conditions.
Want a route through all this instead of an archive? The track
puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.