1. Vampire Numbers.

A vampire number is a composite number with an even number of digits, which can be factored into two numbers (called fangs) that:

• Have the same total number of digits as the original number

• Use all the digits of the original number exactly once

• Do not both end in zero

For 1260:

$$21\times 60=1260$$

• Digits of 1260 → 1, 2, 6, 0

• Digits of fangs (21 and 60) → 2, 1, 6, 0

• Same digits ✔

• Not both fangs end in zero ✔

So 1260 is the smallest vampire number.

Extra facts

• The next vampire numbers include 1395 (15 × 93) and 1435 (35 × 41).

• Vampire numbers were named in 1994 by mathematicians John Conway and Neil Sloane.

2. Eleven plus two trick.

“Eleven plus two” is an anagram of “twelve plus one,” both equaling 13

3.

1 is not a prime number.

Even though it seems like it should be.

4. Fibonacci Sequence.

– Each number is the sum of the previous two: 0, 1, 1, 2, 3, 5… appears in nature (flowers, shells).

5.

Automorphic Numbers:

Numbers whose square ends in the same digits as the number itself (e.g., 5² = 25, 6² = 36, 76² = 5776). 

Automorphic Numbers are numbers whose square ends with the same digits as the number itself.