Observe the following pattern: $1\backslash$times $1=1,11\backslash$times $11=121,111\backslash$times $111=12321,1111\backslash$times $1111=1234321.$ Can you write down the product of $11111\backslash$times $11111$ without the calculator? Why does it work? Does this still pattern extend to a string of $10$ ones? How would you modify it to make it work?