DAY 170
From a plate of cookies, Person A took 1/3 of them, Person B took 1/3 of what was left, and Person C took 1/3 of what was left after Person B. After Person C took his third, 8 cookies remained on the plate. How many cookies were on the plate to start with?

Answer:

27............If X is the number of cookies on the plate when Person C takes his third, then X - 1/3 X = 8. This means there were 12 cookies on the plate before Person C took 4 of them. The equation for Person B would be X - 1/3 X = 12, or 18 cookies on the plate before he took 6 of them. For Person A.........X - 1/3 X = 18, or 27 cookies on the plate before he took 9 of them.

DAY 171
What is the sum of the products in the 9's times table.........(9+18+27+36+45+54+63+72+81+90)?

Answer:

495............By pairing the numbers 0-9/1-8/2-7/3-6/4-5, you get five groups of 9 each = 5 x 9 = 45 in the ones' column, which becomes 49 in the tens' column. Another approach is to realize the products represent 1 nine, two nines, three nines.......up to ten nines. Since the first 10 numbers add up to 55 (ten groups of 11 each), 55 x 9 = 495