Mala has a coloring book in which each English letter is drawn two times.She wants to paint each of these 52 prints with one of the $k$ colors,such that the color pairs used to color any two letters are different.Both prints of the same color can be colored with the same color.What is the minimum number of $k$ that satisfies this requirement?
My progress so far : there is a pair of each letter which can be colored with same color. i.e. $k \cdot k =k^2$ ways to color pair of letters . But Now I don't find way to tackle it further. What is the connection b/w total letters pairs and $k^2$??
More Progress: I came to a conclusion ,see if we have k colors and 26 letters ,and we need every pair of colors to be different ,$k >=26$. But now we have $k^2$ instead of K ,hence $k^2>=26$ might be solution!!
More Progress:But it seems problem of coloring AA,BB.....ZZ is no different than A,B...Z. answer might be $k>=26$