My son requested I made some pages using only level 1 puzzles for my granddaughter to do. You can see and use the first page above, but I’ve also compiled ALL the level 1 puzzles from 2018 and put them in one excel file: Level 1’s from 2018

Those puzzles will give beginners lots of practice and help them learn the multiplication table.

Now I’ll tell you a little bit about the number 1342:

• 1342 is a composite number.
• Prime factorization: 1342 = 2 × 11 × 61
• 1342 has no exponents greater than 1 in its prime factorization, so √1342 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 1342 has exactly 8 factors.
• The factors of 1342 are outlined with their factor pairs in the graphic below.

1342 is the hypotenuse of a Pythagorean triple:
242-1320-1342 which is 22 times (11-60-61)

And (11-60-61) times 122 is a triple where 1342 is a leg:
1342-7320-7442. Pretty cool!

The last prime number was 1327 which was 15 numbers ago. The next prime number won’t be until 1361 which is 19 numbers away. Wow! That means that 1342 is 15 numbers away from the CLOSEST prime number, a new record. Thank you OEIS.org for alerting me to that fact.

Finding the most logical place to start a level 5 puzzle is only a little bit trickier than for a level 4 puzzle. Will you figure it out and not be tricked?

Print the puzzles or type the solution in this excel file: 12 factors 1333-1341

Here is some information about the number 1338:

• 1338 is a composite number.
• Prime factorization: 1338 = 2 × 3 × 223
• 1338 has no exponents greater than 1 in its prime factorization, so √1338 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 1338 has exactly 8 factors.
• The factors of 1338 are outlined with their factor pairs in the graphic below.

1338 is in a couple of Pythagorean triples:
1338-447560-447562 calculated from 2(669)(1), 669² – 1², 669² + 1² and
1338-49720-49738 calculated from 2(223)(3), 223² – 3², 223² + 3²

If you can solve a level 3 puzzle, give this one a try. You will have to locate the best clues to use in the beginning and then what is the most logical clue to use next over and over, but I think you can do that!

Print the puzzles or type the solution in this excel file: 12 factors 1333-1341

Here is some information about the puzzle number, 1337:

• 1337 is a composite number.
• Prime factorization: 1337 = 7 × 191
• 1337 has no exponents greater than 1 in its prime factorization, so √1337 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 1337 has exactly 4 factors.
• The factors of 1337 are outlined with their factor pairs in the graphic below.

1337 is the difference of two squares two ways:
99² – 92² = 1337
669² – 668² = 1337

To solve this level 3 puzzle, start with the clue at the top of the grid, write the factors from 1 to 10 in the appropriate places, then do the same for each factor going down the puzzle row by row.

Print the puzzles or type the solution in this excel file: 12 factors 1333-1341

Here’s some information about the puzzle number, 1336:

• 1336 is a composite number.
• Prime factorization: 1336 = 2 × 2 × 2 × 167, which can be written 1336 = 2³ × 167
• 1336 has at least one exponent greater than 1 in its prime factorization so √1336 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1336 = (√4)(√334) = 2√334
• The exponents in the prime factorization are 3 and 1. Adding one to each and multiplying we get (3 + 1)(1 + 1) = 4 × 2 = 8. Therefore 1336 has exactly 8 factors.
• The factors of 1336 are outlined with their factor pairs in the graphic below.

1336 is the difference of two squares two ways:
335² – 333² = 1336
169² – 165² = 1336

You only need a few clues in the right places to figure out where all the factors from 1 to 12 belong in this mixed up multiplication table puzzle. You can use those clues to put the factors in the right places and solve this one!

Print the puzzles or type the solution in this excel file: 12 factors 1333-1341

• 1334 is a composite number.
• Prime factorization: 1334 = 2 × 23 × 29
• 1334 has no exponents greater than 1 in its prime factorization, so √1334 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 1334 has exactly 8 factors.
• The factors of 1334 are outlined with their factor pairs in the graphic below.

1334 is the hypotenuse of a Pythagorean triple:
920-966-1334 which is (20-21-29) times 46

It is also the leg in a couple of triples:
312-1334-1370 calculated from 29² – 23², 2(29)(23), 29² + 23²
1334-444888-444890 calculated from 2(667)(1). 667² – 1² , 667² + 1²

How well do you know the multiplication table? If you don’t know it very well, this puzzle can be a fun, no-pressure way to get more familiar with it. Give it a try!

Print the puzzles or type the solution in this excel file: 12 factors 1333-1341

Now I’ll share some facts about the puzzle number, 1333:

• 1333 is a composite number.
• Prime factorization: 1333 = 31 × 43
• The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1333 has exactly 4 factors.
• Factors of 1333: 1, 31, 43, 1333
• Factor pairs: 1333 = 1 × 1333 or 31 × 43
• 1333 has no square factors that allow its square root to be simplified. √1333 ≈ 36.51027

1333 is the difference of two squares two different ways:
667²-666² = 1333
37² – 6² = 1333