### Today’s Puzzle:

Write the numbers 1 to 10 in both the first column and the top row so that this level 5 puzzle will function like a multiplication table. Use logic with every step.

### Factors of 1599:

- 1599 is a composite number.
- Prime factorization: 1599 = 3 × 13 × 41.
- 1599 has no exponents greater than 1 in its prime factorization, so √1599 cannot be simplified.
- The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1599 has exactly 8 factors.
- The factors of 1599 are outlined with their factor pair partners in the graphic below.

### More about the Number 1599:

1599 is the hypotenuse of FOUR Pythagorean triples:

276-1575-1599, which is **3** times (92-525-**533**),

351-1560-1599, which is **39** times (9-40-**41**),

615-1476-1599, which is (5-12-13) times **123**, and

924-1305-1599, which is **3** times (308-435-**533**).

1599 is the difference of two squares four different ways:

800² – 799² = 1599,

268² – 265² = 1599,

68² – 55² = 1599, and

40² – 1² = 1599.

Yes, we are just one number away from a perfect square!