Crossword or Death

Algebra Level pending

A crossword puzzle has all of its side lengths as x x letter spaces long. 2 x 2x of those spaces are black, and letters can't go in those spaces. 3 x 3x of the remaining letter spaces in the total area are either filled with the letter a a or letter e e . The amount of a a 's in the crossword is double the amount of the amount of e e 's in the puzzle. If x x = 2 y 2y , and y y = lucky number, how many of the spaces in the crossword puzzle will not be filled in as black or an a a ?


The answer is 140.

Vishruth K by Vishruth K , 13, USA

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1 solution

Vishruth K
Mar 29, 2021
  • For most people, the lucky number is 7.
  • 7 x 2 = 14, so x x = 14
  • 14 x 14 = 196, so there are 196 spaces in the puzzle.
  • 14 x 2 = 28, so 28 spaces are black.
  • 14 x 3 = 42, and 2/3 of those spaces must be a a 's and 1/3 of them must be e e 's to satisfy the condition that the amount of a a 's in the crossword is double the amount of the amount of e e 's in the puzzle. Since 2/3 of those 42 spaces are a a 's, there are 28 a a 's in the puzzle.
  • 28 + 28 = 56
  • 196 - 56 = 140, so 140 spaces in the crossword puzzle aren't filled in black or with an a a .
  • Thus, the answer is 140 .
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