**Important Concepts and Formulas**

1. Numbers can be written in the
generalized form. For a three-digit number, with c in the hundreds place, b in
the tens place and a in the units place, the generalized form would be 100c +
10b + a.

2. The difference between any three-digit
number and number obtained by reversing its digits is always divisible by 99.

3. The sum of all the three-digit
numbers formed using the given three digits is always divisible by 37.

4. The generalized form can be used to
solve puzzles involving numbers.

5. The generalized form helps to explain
the divisibility rules.

6. A number is divisible by

·
2,
if the unit’s digit of the number is 0, 2, 4, 6 or 8.

·
3,
if the sum of the digits of the number is divisible by 3.

·
4,
if the number formed by its digits in the tens place and units place is
divisible by 4.

·
5,
if the unit’s digit is 0 or 5.

·
6,
if the number is even and the sum of the digits of the number is divisible by
3.

·
7,
if the difference between twice the unit’s digit and the number formed by the remaining digits is either 0 or a multiple of 7.

·
8,
if the number formed by its digits in the hundreds place, tens place and units
place is divisible by 8.

·
9,
if the sum of the digits is divisible by 9.

·
10,
if the unit’s digit is 0.

·
11,
if the difference of the sum of its digits in odd places and the sum of its
digits in even places (starting from the units place) is either 0 or divisible
by 11.

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