## Thursday, November 10, 2011

This puzzle arrived from Kim, our expert puzzle solver.  It was on her 7th grader’s last math test:

Add grouping marks (parentheses and/or absolute value symbols) to the following to make the equation true:

-4  +   -8   + 2   *   6  ÷   -6   + 2   + 5   =   2

Answer ideas accepted any time until midnight on Saturday November 12th (EST), on our Family Puzzle Marathon. They will be hidden till then and everyone who submitted something reasonable will get a puzzle point.

Wang said...

(|(|-4| + -8 + 2)| * 6 / (-6 + 2)) + 5 = 2

(|(4 + -8 + 2)| * 6 / (-4) + 5 = 2

(2 * 6 / -4) + 5 = 2

-3 + 5 = 2

For the longest time I couldn't figure out how to get the parentheses to work but now that I read over the question again, it says I can use absolute value symbols as well.

TracyZ said...

When looking at this problem, I was thinking primarily about two aspects of it:
(1) that since all those whole numbers and operations on the left side resulted in an answer of 2, that one of the primary operations was probably the division
(2) The only odd number was the 5 at the end of the left side, and that in general, dividing an even number by another even number can result in an answer that is either odd or even (depending on the numbers involved), so I'd have to look for a division that resulted in an odd number.

I moved the 5 to the right side of the equation, so that
-4 + -8 + 2 * 6 / -6 + 2 = -3
(parentheses and absolute value signs not yet included).

From there, I found two possible solutions:
(|-4| + |-8| + (2 * 6)) / -(6 + 2) = -3
24/-8 = -3

or -(4+|-8| + (2 * 6)) / (|-6| + 2) = -3
-24/8 = 3

so that the original equation could be re-written as:
(|-4| + |-8| + (2 * 6)) / -(6 + 2) + 5 = 2
or -(4+|-8| + (2 * 6)) / (|-6| + 2) + 5 = 2

With both of these, I'm not sure it was entirely "legal" to put the parentheses between the negative sign and the number, but I wasn't able to find any other solutions.

Jerome said...

I would hate to be in grade seven and see that bit of trickery coming at me in a 20 minute quiz especially if it was a bonus question. Was it?

((abs(-4) + abs(-8) + (2*6)) / -(6+2)) + 5 =2
((|-4| + |-8| + (2*6)) / -(6+2)) + 5 = 2

(12 + 12)/(-8) + 5 = 2
24/-8 + 5 = 2
- 3 + 5 = 2
2 = 2

I think the brackets are correct.

By the way, your daughter's name is???

SteveGoodman18 said...

(-4 + abs(-8 + 2)) * 6 / (-6 + 2) + 5 = 2

Absolute value of -8 + 2 is 6. -4 + 6 is 2. 2 times 6 is 12. That 12 is divided by the sum of -6 and 2, which yields -3. -3 + 5 makes 2. Not sure if this is a unique solution or not.

Heidi B said...

I hope I get the notations correct here...

[{|(|-4|+-8+2)|*6}/(-6+2)]+5=2

Annie said...

( [ ( [-4] + -8 +2) * 6] / (-6 + 2) ) +5 = 2

Ilya said...

First of all, congratulations on the arrival of your new baby! Wishing her health and happiness!

Here is one possible answer to the puzzle, I have a feeling there may be more, but my brain hurts to think about it. I am not ready to be in the seventh grade again :-)

||-4| + -8 + 2 * 6 /(-6 + 2) + 5|

anne-marie said...

-4 -8 + 2 *6 : -6 + 2 + 5 =2
-4 - 8 + ((2*6): (-6+2) +5)=2
-4 -8 +(-3+5)=2
-4-8+2=2
-4 + |-8+2|=2
-4 + 6= 2

Maria said...

Xo, everyone seems to have figured this out but not without some trouble. Poor 7 graders! This probably was a bonus question. Many thanks to Kim for sharing this puzzle. All the solutions are slightly different. I think TracyZ deserved two puzzle points for offering two solutions. Everyone else - one point.

anne-marie - at first I didn't understand your solution, but then realized that you introduced abs brackets along the way. If we add them to the second line, it will make sense.

Thank you for your wishes. My daughter's name is Nili (we wanted a Hebrew name that sounds good and doesn't have unpleasant associations on other languages we speak at home - English and Russian, that we like, that kids like, that grandparents like, that is not too common. And my husband wanted it to start with "N." I am surprised she got a name at all with all those constraints :)

Kim said...

Believe it or not, this was not a bonus question. Alas, my poor son was unable to solve it in the time available during the quiz, though he still had to solve it afterwards as part of their post-test review process.

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