A Multiplication Based Logic Puzzle

Posts tagged ‘Star’

987 Christmas Star

Today’s puzzle is a lovely Christmas star whose golden beams shine throughout the dark night. Solving this puzzle could also enlighten your mind.

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

987 is made from three consecutive numbers so it is divisible by 3.

It is also the sixteen number in the Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, . . .

987 is a palindrome when written in base 11 or base 29:
818 in BASE 11 because 8(121) + 1(11) + 8(1) = 987
151 in BASE 29 because 1(29²) + 5(29) + 1(1) = 987

  • 987 is a composite number.
  • Prime factorization: 987 = 3 × 7 × 47
  • 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 987 has exactly 8 factors.
  • Factors of 987: 1, 3, 7, 21, 47, 141, 329, 987
  • Factor pairs: 987 = 1 × 987, 3 × 329, 7 × 141, or 21 × 47
  • 987 has no square factors that allow its square root to be simplified. √987 ≈ 31.416556

 

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332 and a Christmas Star

  • 332 is a composite number.
  • Prime factorization: 332 = 2 x 2 x 83 which can be written 2² x 83
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1) = 3 x 2 = 6. Therefore 332 has exactly 6 factors.
  • Factors of 332: 1, 2, 4, 83, 166, 332
  • Factor pairs: 332 = 1 x 332, 2 x 166, or 4 x 83
  • Taking the factor pair with the largest square number factor, we get √332 = (√4)(√83) = 2√83 ≈ 18.221

Merry Christmas! This is a rather easy level 5 puzzle so I’m sharing it instead of a level 4 puzzle today.

2014-51 Level 4

Print the puzzles or type the factors on this excel file:  10 Factors 2014-12-22

Do You Hear What I Hear? by Noël Regney

Said the night wind to the little lamb,
Do you see what I see
Way up in the sky, little lamb,
Do you see what I see
A star, a star, dancing in the night
With a tail as big as a kite
With a tail as big as a kite

Said the little lamb to the shepherd boy,
Do you hear what I hear
Ringing through the sky, shepherd boy,
Do you hear what I hear
A song, a song, high above the trees
With a voice as big as the sea
With a voice as big as the sea

Said the shepherd boy to the mighty king,
Do you know what I know
In your palace warm, mighty king,
Do you know what I know
A Child, a Child shivers in the cold
Let us bring Him silver and gold
Let us bring Him silver and gold

Said the king to the people everywhere,
Listen to what I say
Pray for peace, people everywhere!
Listen to what I say
The Child, the Child, sleeping in the night
He will bring us goodness and light
He will bring us goodness and light

2014-51 Level 4 Factors

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