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Using only the numbers 3, 3, 3 and 3 once and + - * / once find 7?

  1. Mar 14, 2013 #1
    Hi,

    At the end of our lecture today, the lecturer gave us this simple yet impossible puzzle.

    My friend and I have tried to find the answer but in vain...

    Using only the numbers 3, 3, 3 and 3 once and using only the four arithmetic + - * / once can you make the number 7.

    The closest I have got is 6 or 8 but not 7.

    3*3 all / 3 and then + 3 = 6
    or
    3*3 then - 3/3 = 8

    How to find 7?? Is this actually possible?
     
  2. jcsd
  3. Mar 14, 2013 #2

    phyzguy

    User Avatar
    Science Advisor

    3 + 3 + 3/3 = 7
     
  4. Mar 14, 2013 #3

    jedishrfu

    Staff: Mentor

    think of it in terms of combinatorics with the operators:

    3 op1 3 op2 3 op3 3

    so there's 4 choices for the first, 3 for the third, 2 for the last one = 24 choices

    Phyzguy's solution is almost correct except that he repeated the + operator and the problem says to use each operation once.

    3+3-3*3=-3
    3+3-3/3=5
    3+3*3-3=9
    3+3*3/3=6
    3+3/3-3=1
    3+3/3*3=3.33333

    3-3+3*3=9
    3-3+3/3=1
    3-3*3-3=-9
    3-3*3/3=0
    3-3/3+3=5
    3-3/3*3

    ...
     
  5. Mar 14, 2013 #4
    Can't do 3 + 3 + 3/3 = 7 as you are using + twice
     
  6. Mar 14, 2013 #5
    Are you saying it's therefore impossible?
     
  7. Mar 14, 2013 #6

    jedishrfu

    Staff: Mentor

    I can't tell you the answer only how to think about the problem as it was assigned by your prof.
     
  8. Mar 14, 2013 #7
  9. Mar 14, 2013 #8

    jedishrfu

    Staff: Mentor

    You can't finish the other 12 choices to complete the proof?
     
  10. Mar 14, 2013 #9
    are you sure the prof or you have the correct problem?
    a classic is using 5 "3" and all the operators

    (3*3 + 3)/3 + 3 = 7
     
  11. Mar 14, 2013 #10
    But then you are using + twice too
     
  12. Mar 14, 2013 #11

    rcgldr

    User Avatar
    Homework Helper

    3 and 7 are prime numbers. Any combination of operations you try (except for 3/3) will be a multiple of 3. If you use 3/3 = 1, then you'd have to add or subtract the 3/3 to something else, since multiplying would result in a multiple of 3 again, and dividing would result in a fraction.

    The problem doesn't state if you're allowed to use parenthesis to group operations.

    If you're suppose to used + - * / excactly one, that's four operators, so you'd need five 3's.
     
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