<em>Let's take the </em><em>greatest two-digit number</em><em> as an example.</em>
=> 99
<u>Proving...</u>
99 - (9 x 9) = Two-digit number
=> 99 - 81 = Two-digit number
=> 18 = Two-digit number
<em>Since the </em><u><em>difference</em></u><em> between the </em><em>greatest two-digit number</em><em> and the </em><em>product</em><em> of its digits is a </em><u><em>two-digit number</em></u><em>, the </em><u><em>difference</em></u><em> between the other </em><u><em>two-digit numbers</em></u><em> '10, 11, 12.... 97, 98' and the </em><em>product</em><em> of its digits will always be a </em><u><em>two-digit number,</em></u><em> as the product of its digit is less than the </em><u><em>two-digit number.</em></u>