Occasionally, we hear that the number of Easter eggs that are found is one or two less than the number of eggs that were hidden. Still most of the time, all the eggs and candies do get found. You really have no trouble finding all those goodies, and the Easter Egg Hunt seems like it is over in seconds. You can find Easter Eggs but can you find factors? Here’s an **Easter Basket** Find the Factors 1 – 10 Challenge Puzzle for you. I guarantee it won’t be done in seconds. Can you find all the factors? I dare you to try!

# Puzzles

# 1365 Shamrock Mystery

Beautiful shamrocks with their three heart-shaped leaves are not difficult to find. Finding the factors in this shamrock-shaped puzzle might be a different story. Sure, it might start off to be easy, but after a while, you might find it a wee bit more difficult, unless, of course, the luck of the Irish is with you!

Now I’ll share some information about the number 1365:

- 1365 is a composite number.
- Prime factorization: 1365 = 3 × 5 × 7 × 13
- The exponents in the prime factorization are 1, 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 × 2 = 16. Therefore 1365 has exactly 16 factors.
- Factors of 1365: 1, 3, 5, 7, 13, 15, 21, 35, 39, 65, 91, 105, 195, 273, 455, 1365
- Factor pairs: 1365 = 1 × 1365, 3 × 455, 5 × 273, 7 × 195, 13 × 105, 15 × 91, 21 × 65, or 35 × 39
- 1365 has no square factors that allow its square root to be simplified. √1365 ≈ 36.94591

1365 is the hypotenuse of FOUR Pythagorean triples:

336-1323-1365 which is **21** times (16-63-**65**)

525-1260-1365 which is (5-12-**13**) times **105**

693-1176-1365 which is **21** times (33-56-**65**)

819-1092-1365 which is (3-4-**5**) times **273**

1365 looks interesting in some other bases:

It’s 10101010101 in BASE 2,

111111 in BASE 4,

2525 in BASE 8, and

555 in BASE 16

I’m feeling pretty lucky that I noticed all those fabulous number facts! If you haven’t been so lucky finding the factors of the puzzle, the same puzzle but with more clues might help:

# 1350 Logic is at the Heart of This Puzzle

By simply changing two clues of that recently published puzzle that I rejected, I was able to create a

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

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

# 1349 A Rejected Puzzle

I was in the mood to make a Find the Factors Challenge Puzzle that used the numbers from 1 to 12 as the factors. I’ve never made such a large puzzle before, but after I made it, I rejected it. All the puzzles I make must meet certain standards: they must have a unique solution, and that solution must be obtainable by using logic. Although the “puzzle” below has a unique solution, and you can fill in a few of the cells using logic, you would have to use guess and check to finish it. Besides that, you wouldn’t be able to know if you guessed right until almost the entire puzzle was completed. Thus, it doesn’t meet my standards.

Even though the puzzle was rejected, there were still some things about it that I really liked. In my next post, I’ll publish a slightly different puzzle that uses some of the same necessary logic that I appreciated but doesn’t rely on guess and check at all. This is NOT the first time I have tweaked a puzzle that didn’t initially meet my standards to make it acceptable. I just thought I would share the process this time. If you try to solve it, you will be able to see the problem with the puzzle yourself.

Now I’ll share some information about the number 1349:

1349 is the sum of 13 consecutive primes, and it is also the sum of three consecutive primes:

73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 = 1349

443 + 449 + 457 = 1349

# 1332 Yet Another Christmas Tree

Here is yet another Christmas tree for you to enjoy this holiday season.

# 1329 Flight Plans

Many people fly home or away from home for the holidays. Here’s a puzzle to occupy some of your time while you’re in flight.

# 1328 Christmas Tree

Can you figure out where to put the numbers from 1 to 10 in both the first column and the top row so that the lights on this Christmas tree work properly?

# 1325 Hockey Stick

If someone you know loves hockey and wants a fun way to practice multiplication facts, this hockey stick could be the perfect gift.

# 1324 Gingerbread Man

The Gingerbread man can be tricky so be careful while solving this puzzle. He has fooled and run away from many different people and animals. The mystery is can YOU outfox this one?

# 1322 Christmas Star

The first Christmas Star led the wise men to find the Baby Jesus.

This Christmas star can lead you to a better knowledge of all the facts in a basic 1 to 10 multiplication table.