Hints and solutions to Look for a pattern #10

1990 - 1980 + 1970 - 1960 + ..... - 20 + 10 = ?

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• Let's simplify the problem and take a little at a time, starting from the end of the sum:
  30 - 20 + 10 =10 + 10 = 20
  50 - 40 + 30 - 20 + 10 = 10 + 10 + 10 = 30
  70 - 60 + 50 - 40 + 30 - 20 + 10 = ... = 40
  and so forth

  So we add another 10 for each pair of numbers that goes on the front.

• How many pairs of numbers do we add to get all the way to 1990? (The 10 at the end doesn't count).
• Well, 2 x 99 = 198, so it looks like there are 99 pairs of numbers and then the 10 at the end. So the total is 99 x 10 + 10 = 100 x 10 = 1,000.

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