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Sawing Wood With Elation!

Why is it that we jump with elation when we discover math errors? For example, I recently waited patiently in a pita-sandwich shop while the staff filled in all the decimal points (using appriopriate colors) in their special signs...i.e. changing .95 to 95. Not sure they appreciated my business!

Another source of ready errors is on standardized tests. For example, consider this question taken from a sample test in the review manual for the PSAT:

A board 7 feet 9 inches long is divided into three equal parts. What is the length of each part?

  • 2 ft. 7 in.
  • 2 ft. 6 1/3 in.
  • 2 ft. 8 1/3 in.
  • 2 ft. 8 in.
  • 2 ft. 9 in.
Now, I realize that you (and I) know the right "obvious" answer...but that is not my point (or my jump for elation).

Your Task: Think creatively...Can you think of other correct answers not displayed as options? For example, how could 7 ft. 9 in. be a correct answer...in multiple ways? How many new unique answers can you create?

Your New Task: Is it possible for for each of given answers in the problem to be correct?

Note 1: One difficulty is the meaning of the word "equal" in the problem as stated. Does it mean congruent in shape...or equal in area...or?

Note 2: Another difficulty is the interpretation of the word "board." Must we assume that all boards are rectangular parallelpipeds?

Perhaps this question should be discarded...


Source: E. Steinberg's PSAT-NMSQT, 1985, p. 239

Hint: Think of different ways (directions?) one can sawe a "board"? Do the cuts have to be straight?


Solution Commentary: Sorry, I will let you evaluate your own creative solutions.