A 9 years old girl in 1941 has written each of the times tables up to 10 on her Golden Rod tablet. She did that because she has to memorize them. Her dad, (with the best of intentions) insists she has to recite the multiplication tables through 10 before she can eat dinner. Its been a long trek and she hasn't succeeded yet. Each night her sisters and brother giggle while she haltingly begins; 1 x 1 = 1; 1 x 2 = 2; etc., attempting to get through to 10 x 10 = 100. Her dinner is delayed every evening. Looking at the paper a thought occurs into her mind: "Add the double numbers in each product, across." She seems to know what that means, 2,4,6,8,10,12,14,16, 18, 20 becomes 2,4,6,8,1,3,5,7,9,2... The table of 3's: 3,6,9,12,15,18,21,24, 27 30 becomes 3,6,9,3,6,9,3,6,9,3... She sees that each times table has a hidden pattern that repeats and the table of 9's is extremely easy because each product sums to 9! But at a certain point right in the middle: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 the numbers twist around, 45 becomes 54, the numbers repeat but are reversed. That's nice, she thinks.