A Multiplication Based Logic Puzzle

Archive for the ‘Level 1 Puzzle’ Category

1031 Prepare for World Maths Day 2018

You might think that a day lasts 24 hours, but strategic use of the international date line can actually make a single day last 48 hours!

How will you spend the 48 hour day that will be 7 March 2018?

Colleen Young encourages you and your class to register for and participate in World Maths Day 2018 held that day. She shares the necessary links as well as several tips on how to prepare.

One way to prepare now is playing multiplication games like the level 1 puzzle below. The puzzle is just a multiplication table but the factors are missing and only a few of the products are given, and they aren’t in the order you would normally expect. Can you figure out where the factors from 1 to 12 belong in both the first column and the top row of the puzzle?

Print the puzzles or type the solution in this excel file: 12 factors 1028-1034

If this puzzle is too easy for you, Then it is time to move on to a level 2 or higher puzzle. You can find one in the link above and plenty others here at findthefactors.com.

Now I’d like to tell you some things that I’ve learned about the number 1031:

1031 and 1033 are twin primes.

1031 is a palindrome in a couple of bases:
It’s 858 in BASE 11 because 8(121) + 5(11) + 8(1) = 1031 and
it’s 272 in BASE 21 because 2(441) + 7(21) + 2(1) = 1031

  • 1031 is a prime number.
  • Prime factorization: 1031 is prime.
  • The exponent of prime number 1031 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1031 has exactly 2 factors.
  • Factors of 1031: 1, 1031
  • Factor pairs: 1031 = 1 × 1031
  • 1031 has no square factors that allow its square root to be simplified. √1031 ≈ 32.10919

How do we know that 1031 is a prime number? If 1031 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1031 ≈ 32.1. Since 1031 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1031 is a prime number.

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1012 Do Your Brain a Favor

Do your brain a favor by completing puzzles in 2018. This one is a great place to start, and 20 18 is actually included in the clues. You can turn this puzzle into a multiplication table if you can write the numbers from 1 to 12 in the first column and also in the top row in the correct places. Then you will be able to fill in the rest of the cells in the table by remembering multiplication facts you’ve already learned. It will be fun and good for your brain.

1002 Merry Christmas!

Merry Christmas, everyone!

No matter what is going on in your life, may your day today be filled with love, peace, and joy.

Print the puzzles or type the solution in this excel file: 10-factors-1002-1011

1002 is the sum of the eighteen prime numbers from 19 to 97.
It is also the sum of two consecutive prime numbers:
499 + 503 = 1002

1002 is a palindrome in two other bases:
6B6 in BASE 12 (B is 11 base 10)
2A2 in BASE 20 (A is 10 base 10)

  • 1002 is a composite number.
  • Prime factorization: 1002 = 2 × 3 × 167
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1002 has exactly 8 factors.
  • Factors of 1002: 1, 2, 3, 6, 167, 334, 501, 1002
  • Factor pairs: 1002 = 1 × 1002, 2 × 501, 3 × 334, or 6 × 167
  • 1002 has no square factors that allow its square root to be simplified. √1002 ≈ 31.65438

994 and Level 1

All you need is these eleven clues and the multiplication facts in a normal 12 × 12 multiplication table to completely fill in every square of this abnormal multiplication table, I mean puzzle. Don’t worry about how fast you can solve the puzzle. The more puzzles you solve the better you will get at doing them. Relax and enjoy yourself!

Print the puzzles or type the solution in this excel file: 12 factors 993-1001

When is the number 994 a palindrome?
It is 4334 in BASE 6 because 4(6³) + 3(6²) + 3(6¹) + 4(6⁰) = 994, and
it’s 464 in BASE 15 because 4(15²) + 6(15¹) + 4(15⁰) = 994

  • 994 is a composite number.
  • Prime factorization: 994 = 2 × 7 × 71
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 994 has exactly 8 factors.
  • Factors of 994: 1, 2, 7, 14, 71, 142, 497, 994
  • Factor pairs: 994 = 1 × 994, 2 × 497, 7 × 142, or 14 × 71
  • 994 has no square factors that allow its square root to be simplified. √994 ≈ 31.52777

986 and Level 1

Today’s puzzle looks like a simple holiday napkin, and it’s actually quite simple to solve. Even kids who have learned how to multiply but haven’t even heard of division could solve this puzzle.

Print the puzzles or type the solution in this excel file: 10-factors-986-992

986 looks the same upside-down as it does right-side up, so it is a strobogrammatic number.

31² + 5² = 986
25² + 19² = 986

986 is the hypotenuse of FOUR Pythagorean triples:
264-950-986
310-936-986
680-714-986
464-870-986

986 looks interesting in some other bases:
12421 BASE 5
TT in BASE 33 (T is 29 base 10)
T0 in BASE 34

  • 986 is a composite number.
  • Prime factorization: 986 = 2 × 17 × 29
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 986 has exactly 8 factors.
  • Factors of 986: 1, 2, 17, 29, 34, 58, 493, 986
  • Factor pairs: 986 = 1 × 986, 2 × 493, 17 × 58, or 29 × 34
  • 986 has no square factors that allow its square root to be simplified. √986 ≈ 31.4006

978 A Gift-Wrapped Puzzle

Today’s puzzle comes gift-wrapped just for you. Figuring out the solution to this puzzle is about as easy as ripping gift-wrap off a present, too. What is the common factor in both parts of the ribbon? There is only one answer to that question that will not put any numbers greater than 12 where the factors go. So put the factors of the clues in the first column and top row so that this puzzle becomes a multiplication table (but with the factors in a different order than usual).

Print the puzzles or type the solution in this excel file: 12 factors 978-985

Here are some facts about the number 978:

It is made from 3 consecutive numbers, 7-8-9, so it is divisible by 3.

Stetson.edu reminds us that it is the sum of four consecutive fourth powers:
2⁴ + 3⁴ + 4⁴ + 5⁴ = 978

 

It is the sum of two consecutive prime numbers:
487 + 491 = 978

I like the way it looks when written in a couple of other bases:
Palindrome 696 in BASE 12 because 6(12²) + 9(12) + 6(1) = 978
369 in BASE 17 because 3(17²) + 6(17) + 9(1) = 978

  • 978 is a composite number.
  • Prime factorization: 978 = 2 × 3 × 163
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 978 has exactly 8 factors.
  • Factors of 978: 1, 2, 3, 6, 163, 326, 489, 978
  • Factor pairs: 978 = 1 × 978, 2 × 489, 3 × 326, or 6 × 163
  • 978 has no square factors that allow its square root to be simplified. √978 ≈ 31.27299

 

970 and Level 1

This level 1 puzzle will help you focus on one set of division facts. You can find all the factors that belong in the first column and the top row if you know those division facts. After you find all the factors from 1 to 10, you can fill in the entire multiplication table.

Print the puzzles or type the solution in this excel file: 10-factors-968-977

970 is the sum of two squares two different ways:
23² + 21² = 970
31² + 3²= 970

That means 970 is the hypotenuse of more than one Pythagorean triple:
88-966-970 calculated from 23² – 21², 2(23)(21), 23² + 21²
186-952-970 calculated from 2(31)(3), 31² – 3², 31² + 3²
582-776-970 which is (3-4-5) times 194
650-720-970 which is 10 times (65-72-97)

Here’s a fun fact: 970 is 202 in BASE 22 because 2(22²) + 2(1) = 2(484 + 1) = 2(485) = 970

  • 970 is a composite number.
  • Prime factorization: 970 = 2 × 5 × 97
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 970 has exactly 8 factors.
  • Factors of 970: 1, 2, 5, 10, 97, 194, 485, 970
  • Factor pairs: 970 = 1 × 970, 2 × 485, 5 × 194, or 10 × 97
  • 970 has no square factors that allow its square root to be simplified. √970 ≈ 31.14482

 

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