12^2 = 144

21^2 = 441

13^2 = 169

31^2 = 961

## Wednesday, March 9, 2011

### Geometry Challenge

Take any parallelogram. Construct squares on each side of the parallelogram. Prove that the centers of the constructed squares form a square.

## Tuesday, March 8, 2011

### 0.99999... = 1

Let x = 0.99999...

10x = 9.99999...

10x - x = 9.99999... - 9 = 9

9x = 9

x = 1

Do you believe?

10x = 9.99999...

10x - x = 9.99999... - 9 = 9

9x = 9

x = 1

Do you believe?

### Log problem

log 237.5812087593 = 2.375812087593 (approximately)

What is the pattern here? Can you write an equation for this that 2.375812087593 solves? The equation has exactly one other solution. What is the other solution? Can you prove that these are the only two solutions?

(This is beyond the scope of the SAT Reasoning Test, but is reasonably related to the SAT Math 2 subject test.)

What is the pattern here? Can you write an equation for this that 2.375812087593 solves? The equation has exactly one other solution. What is the other solution? Can you prove that these are the only two solutions?

(This is beyond the scope of the SAT Reasoning Test, but is reasonably related to the SAT Math 2 subject test.)

### Digits Problem

Each letter represents a digit. Solve for the digits and numbers.

TWO + THREE + SEVEN = TWELVE

TWO + THREE + SEVEN = TWELVE

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