1763 Daffodil Puzzle

Today’s Puzzle:

Spring has sprung and perhaps flowers are blooming in your area. I think my favorite flowers are daffodils. I love the way they are shaped and their vibrant colors.

This daffodil puzzle is a great way to welcome spring. It may be a little bit tricky, but I think if you carefully use logic you will succeed! Just write each of the numbers 1 to 12 in the first column and again in the top row so that those numbers are the factors of the given clues. As always there is only one solution.

Here’s the same puzzle if you’d like to print it using less ink:

Factors of 1763:

  • 1763 is a composite number and the product of twin primes.
  • Prime factorization: 1763 = 41 × 43.
  • 1763 has no exponents greater than 1 in its prime factorization, so √1763 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 1763 has exactly 4 factors.
  • The factors of 1763 are outlined with their factor pair partners in the graphic below.

More About the Number 1763:

1763 is the difference of two squares in two different ways:
882² – 881² = 1763, and
42² – 1² = 1763. (That means the next number will be a perfect square!)

1763 is the hypotenuse of a Pythagorean triple:
387-1720-1763, which is (9-40-41) times 43.

1763 is palindrome 3E3 in base 22 because
3(22²) + 14(22) + 3(1) = 1763.

Lastly and most significantly: 15, 35, 143, 323, 899, and 1763 begin the list of numbers that are the product of twin primes. 1763 is just the sixth number on that list! If we include the products of two consecutive primes whether they are twin primes or not, the list is still fairly small. How rarely does that happen?

When it was 2021, did you realize how significant that year was?