Anton writes down all positive integers in sequence that are divisible by 2. Berta writes down all positive integers in sequence that are divisible by 3. Clara writes down all positive integers in sequence that are divisible by 4. The orderly Dora notes the numbers written down by the others. She orders the numbers by size and does not write any number more than once. What is the 2017th number in her list?

(Richard Henner)
(Richard Henner) Clara's numbers can be omitted by Dora because they have all already been written by Anton. Of the numbers up to 3000, Anton has written 1500 and Berta 1000, 500 of which have been written by both and are therefore omitted by Dora. Dora thus writes exactly 2000 numbers up to 3000. The next 17 numbers are 3002, 3003, 3004, 3006, 3008, 3009, 3010, 3012, 3014, 3015, 3016, 3018, 3020, 3021, 3022, 3024, 3026. 3026 is thus the last number that Dora writes.