5
Part of 2017 May Olympiad
Problems(2)
shortest words in 2 letter language (Olimpiada de Mayo) 2017 L2 P5
Source:
9/24/2021
Ababa plays with a word made up of the letters of his name and has set certain rules:
If you find an followed immediately by a , you can substitute for them.
If you find two consecutive 's, you can delete them.
If you find three consecutive 's, you can delete them.
Ababa begins with the word .
With the above rules, how many letters do you have the shortest word you can come up with?
Why can't you come up with one more word shorter?
combinatorics
24 pos. integers wanted, a+b divides ab 2017 May Olympiad L1 p5
Source:
8/25/2021
We will say that two positive integers and form a suitable pair if divides (its sum divides its multiplication). Find positive integers that can be distribute into suitable pairs, and so that each integer number appears in only one pair and the largest of the numbers is as small as possible.
number theorydividesdivisible