110. Digital Coincidences. If I multiply two nines and add 9 and 9, I get 81 and 18 - two numbers consisting of the same digits. If I multiply and add 2 and 47, I get 94 and 49 - numbers with the same digits. If I multiply and add 3 and 24, I get 72 and 27 - two numbers consisting of the same digits.

Can you find two numbers, multiplying and adding which you would get two new numbers with three identical digits? The problem has two solutions.
110. If we multiply 497 by 2, we get 994. If we add these two numbers, we get 499. The digits in both cases are the same. A similar result holds for 263 and 2. We get 526 and 265, respectively.

[G. Lindgren points out that by introducing nines after the first digit, one can obtain two answers with any desired number of digits: \(4997+2=4999 ; 4997 \times 2=9994 ; 2963+2=2965 ; 2963 \times 2=5926\); similarly for \(49997+\) (or \(\times) 2 ; 29963+\) (or \(\times\) ) 2, and so on. - M. G.]