# 1689 Candy Corn Again?!

### Today’s Puzzle:

Here’s yet one more candy corn puzzle. You would think it was everyone’s favorite kind of candy the way it is represented on this blog! This puzzle is level 6, so you will probably find it more difficult to solve. Using logic, write the numbers from 1 to 12 in both the first column and the top row so that those numbers and the given clues form a multiplication table.

### Factors of 1689:

• 1689 is a composite number.
• Prime factorization: 1689 = 3 × 563.
• 1689 has no exponents greater than 1 in its prime factorization, so √1689 cannot be simplified.
• The exponents in the prime factorization are 1 and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1689 has exactly 4 factors.
• The factors of 1689 are outlined with their factor pair partners in the graphic below.

### More About the Number 1689:

1689 is the difference of two squares in two different ways:
845² – 844² = 1689, and
283² – 280² = 1689.