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Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

ARITH-Maze puzzle

In the following ARITH-Maze puzzle, go to ‘START’ and proceed through this numerical maze, following instructions as provided, until you get to the ‘FINISH’ box. What number did you finish with?

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Last month's solutions
  1. How many complete turns does circle A make to rotate around the outside of circle B once if circle A is one-half the size of circle B. (Note: Diagram is not drawn to scale.)

Solution:

Note: As circle A rotates once around the outside of stationary circle B, circle A rotates 720º (or 2 to1 as if the length of the circumference of circle B was laid flat as a straight line plus another 360º as it relates to the one rotation around the exterior of circle B. Therefore, circle A rotates a full 1080º (720º + 360º) or 3 complete turns.

  1. How many complete turns does circle A make to rotate around the inside of circle B once if circle A is one-half the size of circle B. (Note: Diagram is not drawn to scale.)

Solution: 

Note: As circle A rotates once around the inside of stationary circle B, circle A rotates 720º or 2 to 1 as if the length of the circumference of circle B was laid flat as a straight line minus 360º as it relates to the one rotation around the internal of circle B. Therefore, circle A rotates a full 360º (720º – 360º) or 1 complete turn.

 

  1. To get a square photograph to fit into a rectangular frame, Brian had to trim a 1-inch strip from each of two opposite sides of the photo and a 2-inch strip from each of the other two sides. In all, he trimmed of 64 squire inches. What were the original dimensions of the photograph?

Solution:

Let X = the side dimension of the square photograph
Then, Area of two 1-inch trims = 2 * (H1 * W1) = 2 * (1 * x) = 2x
and, Area of two 2-inch trims = 2 * (H2 * W2) = 2 * [(x-2) * 2] = 4x – 8
Therefore, (2x) + (4x – 8) = 64, 6x = 64 + 8 = 72, x = 72/6 = 12
The original dimensions of the photograph was 12 x 12 inches.

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