Sandy Wood
Brain Game: Math Square #8
by Sandy Wood - January 4, 2010 - 7:30 AM

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Welcome to a brand new year of mental_floss Brain Games. Here’s one to get 2010 started with a bang:

The nine white squares inside the main red grid should be filled with the digits 1 through 9. Each digit should appear only once in this main grid. Two of these numbers are already provided for you. Place the other digits in the correct spots so that the mathematical equations work both across and down. IMPORTANT: Remember algebraic rules when solving the problems… multiplication and division should be performed in the first step, then addition and subtraction in the second. Good luck!

mathsq-08-q

Here is the SOLUTION.

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Comments (8)

  1. Not too hard at all, and it’s nice to start my Monday with a small feeling of accomplishment.

    posted by B on 1-4-2010 at 10:55 am

  2. Since when does 7-6/2=4? 7-6=1 1/2=2

    Where does 4 come into the equation?

    posted by hannah on 1-4-2010 at 11:34 am

  3. Since when does 3+8*9=75?

    3+8 = 11
    11*9= 99

    posted by hannah on 1-4-2010 at 11:36 am

  4. Hannah, 7 – 6/2 = 4 because of the order of operations (as explained in the rules).

    7 – (6/2) = 7 – 3 = 4

    3 + (8*9) = 3 + 72 = 75

    posted by Linton on 1-4-2010 at 11:41 am

  5. “IMPORTANT: Remember algebraic rules when solving the problems… multiplication and division should be performed in the first step, then addition and subtraction in the second.”

    posted by SlackJack on 1-4-2010 at 12:31 pm

  6. Of course, I like doing it the hard way:

    If we assign letters (a through i) for the missing spaces, then we have the following equations:

    1: a + 4 + c = 14
    2: d + e + f = 15
    3: g – 5 + i = 6
    4: a + dg = 75
    5: 4 – e + 5 = 8
    6: c – f/i = 4
    Simplifying
    1a: a + c = 10
    3a: g + i = 11
    *5a: e = 1
    7: We know that a and c are members of the set (2,8) or (3,7)
    8: We know that g and i are members of the set (2,9) or (3,8)
    9: We know that d and f are members of the set (6,8)
    Therefore, since d or f is 8,
    7a: We know that a and c are members of the set (3,7)
    8a: We know that g and i are members of the set (2,9)
    10: Since f/i is an integer and f is either 6 or 8, we know that f and i are members of the set (2,8) or (2,6)
    **11: Therefore, i = 2
    ***12: Therefore, g = 9
    4a: a + 9d = 75
    ****4b: The next divisible-by-9 integer lower than 75 is 72. Thus, 9d = 72 = 75 – 3. Therefore a = 3
    *****13: 9d = 72, d = 8
    ******14: f = 6
    *******15: c = 7

    QED, no guesswork involved.

    And, yes, I know it is harder to do it this way, but I can’t help it if it makes me feel better.

    posted by Izzy on 1-4-2010 at 1:26 pm

  7. Hannah, not only does the order of operations matter, 1/2 does not equal 2, it equals .5

    And Izzy, fear not, I always solve these that same way, you aren’t alone :P

    posted by Luke on 1-4-2010 at 10:00 pm

  8. Your BEDMAS is all messed up for the centre column; addition comes before subtraction therefore 5+1-4 cannot equal 8.

    posted by MJJY on 3-10-2010 at 12:08 pm

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