8
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Challenge

Solve the following equations by converting to standard form (see below):

  • ** eeeeee = aeeeeiiiouu
  • ** eeeeee = aeeeoouuu
  • -/ eeeo = i
  • *- eeooo = eeee
  • / aeiou = aeeioouu
  • /+/ eiiiiii = eo

Brief Overview

This is essentially a cross between a math puzzle and a word puzzle. I'll explain how this works by going backwards from a solution.

  1. Start with an elementary equation:
    1+1*2=3
  2. In English, this can be written:
    one+one*two=three
  3. Remove all consonants:
    oe+oe*o=ee
    (Note: aeiou are the only vowels wrt this puzzle)
  4. Move vowels to the end of each side of the = and sort:
    +* eeooo = ee

Again, you're going the other way; you are given form 4. above, and expected to find form 1. (or 2.).

That is, the answer to: +* eeooo = ee
is: 1+1*2=3

Details

Rules followed by the puzzle format:

  • Multiplication (*) and division (/) collectively are performed left to right.
    For example, 9*4/6*236/6*26*212.
  • Addition (+) and subtraction (-) are then performed left to right in a similar manner.
  • All operands are positive integers.
  • All intermediate results are also positive integers.
    For example, 2/4*2 will never appear in a solution because 2/4 is performed first, and this is not a positive integer.
    Likewise, 3-4+5 will not appear because 3-4 is not a positive integer.
  • Numbers are in formal American English form.
    Briefly, don't use the article "a" or the conjunction "and" in number names; 101 is spelled one hundred one.
  • Per the rules of this puzzle, answers that commute into each other (to form the same operator set) are considered equivalent.
    For example, if j*k+l*m works for some j k l m, l*m+k*j is considered the same answer.
  • Notwithstanding the above equivalence principle, the solution to all challenge problems is unique.
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5
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1.

70*12*7=5880

3.

70-20/2=60

4.

42*2-7=77

5.

50000/20=2500

6.

96/6+36/6=22

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  • $\begingroup$ I think 3 might be wrong. The question has three e's on the left while yours has four. +1 for the others though. $\endgroup$ – hexomino May 1 '18 at 8:53
  • $\begingroup$ @hexomino You're right, I miscounted. Fixed it. $\endgroup$ – noedne May 1 '18 at 8:54
  • $\begingroup$ Vowel counts don't match for one of your answers. $\endgroup$ – H Walters May 1 '18 at 13:45
  • $\begingroup$ @HWalters Thanks, I forgot the teen. $\endgroup$ – noedne May 1 '18 at 18:07
5
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It looks like 2 is still open?

10 * 17 * 20 = 3400

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