total number of alphanumeric letter = $26$
Each is printed twice the no. of letters = $26×2$ = $52$
case 1: If Mala has $ k$ colors, she can have k pairs of same colors.(red,red),(blue,blue)...etc
case 2: She also can have $kc_{2}$ different pairs in which each pair is having different colors.(blue,green),(red,green)...etc
k colors let pairs (a,b) can be choose with k color and b can be choose with k-1 color=$k*(k-1)$
and (a,b) (b,a) is same thing we divide by 2
$k*(k-1)/2$=$kc_{2}$
So minimum no. of colors, so that we could color all 26 letters.=$case 1+case 2\geqslant26$
$k+kc_{2} ≥ 26$
$k+k(k-1)/2 ≥ 26$
$k(k+1)/2 ≥ 26$
$k(k+1) ≥ 52$
$k(k+1) ≥ 7*8$
$k≥7$