Question 1203985
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There is a painting using two colors: it is the chessboard painting.


From the other side, one color does not produce any solution.


Hence, two colors is the least number of different colors that is needed.




It is a standard, traditional, complete and mathematically absolutely correct reasoning and a solution.




See similar solutions at this forum under these links


https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1096043.html


https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1095728.html



This problem is known for hundreds of years. With a similar solution, it is written and placed 
in hundreds of textbooks in Math in different languages, that are collections of entertainment problems. 
So far, I never heard  that somebody would be unsatisfied or expressed doubts in validity of this solution.
In opposite, the normal human reaction is admiration that so simple and so elegant solution is possible.
You are the first person who expresses your unsatisfaction  (due to unknown reason).  My congratulations  ( ! )