Calendar Square of Dates: Formula

Take a calendar, and draw a square around any nine dates (it will be a 3 x 3 square, right?) Let s be the smallest number in the square. If you add up all the numbers in the square, the answer will always be a multiple of 9. In particular, the sum will be exactly 9 · (s + 8). Why?

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Tie-Dyed T-Shirts

On Earth Day, in Wilder Bowl, Emily had 30 tie-dyed t-shirts to sell at the rate of 3 for $20.00. Liz had 30 slightly fancier t-shirts to sell at the rate of 2 for $20.00. Emily suddenly got sick and asked Liz to sell her shirts for her. Liz agreed. Finding the difference in price a bit hard to keep track of, Liz decided to combine everything and sell all the shirts at 5 for $40.00, a reasonable decision. After everything sold out, which it did, Liz dropped off Emily’s $200. But then, to her surprise, instead of the $300 she expected to have left for herself, she had only $280. What happened to the other $20.00?

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