By simply changing two clues of that recently published puzzle that I rejected, I was able to create a love-ly puzzle that can be solved entirely by logic. Can you figure out where to put the numbers from 1 to 12 in each of the four outlined areas that divide the puzzle into four equal sections? If you can, my heart might just skip a beat!

If you need some tips on how to get started on this puzzle, check out this video:

Now I’ll tell you a few things about the number 1350:

- 1350 is a composite number.
- Prime factorization: 1350 = 2 × 3 × 3 × 3 × 5 × 5, which can be written 1350 = 2 × 3³ × 5²
- The exponents in the prime factorization are 1, 3 and 2. Adding one to each and multiplying we get (1 + 1)(3 + 1)(2 + 1) = 2 × 4 × 3 = 24. Therefore 1350 has exactly 24 factors.
- Factors of 1350: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675, 1350
- Factor pairs: 1350 = 1 × 1350, 2 × 675, 3 × 450, 5 × 270, 6 × 225, 9 × 150, 10 × 135, 15 × 90, 18 × 75, 25 × 54, 27 × 50 or 30 × 45
- Taking the factor pair with the largest square number factor, we get √1350 = (√225)(√6) = 15√6 ≈ 36.74235

1350 is the sum of consecutive prime numbers two ways:

It is the sum of the fourteen prime numbers from 67 to 131, and

673 + 677 = 1350

1350 is the hypotenuse of two Pythagorean triples:

810-1080-1350 which is (3-4-**5**) times **270**

378-1296-1350 which is (7-24-**25**) times **54**

1350 is also the **20**th nonagonal number because **20**(7 · **20** – 5)/2 = 1350