### Brain Teasers

# Divisible by 23

I'm divisible by 23 and 3.

Count from 1 to 100, and you'll meet the two-digit number in my thousands and hundreds place just before the two-digit number in my tens and ones place.

I'm greater than 2,000, but less than 9,000.

What number am I?

Count from 1 to 100, and you'll meet the two-digit number in my thousands and hundreds place just before the two-digit number in my tens and ones place.

I'm greater than 2,000, but less than 9,000.

What number am I?

### Hint

Using the second clue, make a list of possibilities and use a calculator to check for divisibility.### Answer

The number is 2829.Since the number is between 2,000 and 9,000, the smallest possible digit in the thousands place is 2. The number has to be divisible by 69 (the common multiple of 3 and 23). Using a calculator, you can start with the smallest number that answers the description in the second clue, 2021, and check. None of 2021, 2122, 2223, 2324, 2425, 2526, 2627, 2728 is divisible by 69, and 2829=69*41.

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