1331 is the third row of Pascal’s triangle. What does that mean?

It means that 11³ = 1331,

and it means that 1 + 3 + 3 + 1 = 8 = 2³

Those third powers are not a coincidence.

It means that (x + y)³ = 1x³yº + 3x²y¹ + 3x¹y² + 1xºy³ or written more simply,

(x + y)³ = x³ + 3x²y¹ + 3x¹y² + y³

Likewise, (x – y)³ = 1x³yº – 3x²y¹ + 3x¹y² – 1xºy³ or simply

(x – y)³ = x³ – 3x²y¹ + 3x¹y² – y³

It also means that if you flip a coin three times, you’ll get

three heads and no tails 1 way: (HHH),

two head and one tail 3 ways: (HHT); (HTH); (THH),

one head and two tails 3 ways: (HTT); (THT); (TTH), and

no heads and three tails 1 way: (TTT).

That’s just some of what that third row being 1331 means but here are a few more facts about the number 1331.

- 1331 is a composite number.
- Prime factorization: 1331 = 11 × 11 × 11, which can be written 1331 = 11³
- The exponent in the prime factorization is 3. Adding one, we get (3 + 1) = 4. Therefore 1331 has exactly 4 factors.
- Factors of 1331: 1, 11, 121, 1331
- Factor pairs: 1331 = 1 × 1331 or 11 × 121
- Taking the factor pair with the largest square number factor, we get √1331 = (√121)(√11) = 11√11 ≈ 36.48287
- 1331 is a perfect cube.

1331 is cool in some other bases, too:

It is 1000 in BASE 11, and

it’s 131 in BASE 35