1998 CEMC Gauss (Grade 7) Problems/Problem 18
Problem
The letters of the word ‘GAUSS’ and the digits in the number ‘1998’ are each cycled separately and then numbered as shown: If the pattern continues in this way, what number will appear in front of GAUSS 1998?
Solution
"GAUSS" has 5 letters, so the sequence will reset itself every 5 terms. "1998" has 4 numbers, so the sequence will reset itself every 4 terms. The LCM of 4 and 5 is 20, so the answer is