How fast can you add the first 1000 positive integers? No calculators allowed (it would take too long, anyway, with a calculator.)

First, take out your stop watch, *ie* cell phone.

Ready?

Start!

Hint Think pairs of numbers. And Gauss!

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# Math of the Day

#### How many fractions of type ^{1a9b}/_{1x23y} can be simplified by 44?

Daily morsels of math

How fast can you add the first 1000 positive integers? No calculators allowed (it would take too long, anyway, with a calculator.)

First, take out your stop watch, *ie* cell phone.

Ready?

Start!

Hint Think pairs of numbers. And Gauss!

Hint 44 has to divide both1a9band1x23y. But 44 =4 * 11, therefore 4 and 11 must divide both1a9band1x23y. What are the divisibility rules for 4 and 11?

Can you add two more lines so you have a total of 10 triangles?

Hint The two lines should be intersecting inside the given triangle.