Can You Solve?

[Gregory Matthews]

Given the following set of numbers, can you determine the missing number that should replace the  ?.

99   45   39   36   28   21

72   27    18   21     ?    13   7    

The above logic problem was created by Nob Yoahigahara, and published, on page 26, in The Great Courses Mathematical Brain Teasers and Logic Puzzles, by Jason Rosenhouse, Phd. This is a video course.  If you like it, you may want to consider taking some of the 900+ courses that they offer.

At a later time, I will provide you with the answer.  The answer is simple enough that an 8th grade student will have the skills needed to solve the problem.  Yet, most people cannot solve it

NOTE:  The above set of numbers does not contain a typo.  All listed numbers are correct.

NOTE:  I have a personal bias in favor of The Great Courses.  They produce instructional material in a video format that I believe is of value to people who do not need formal recognition for taking the course-work.  I have personally taken a number of their courses, some of which have been in the area of religion, and others have been in the area of science.

[Gregory Matthews]

Hint:  if you do not consider the number 7, in the above listing, there are two possible solutions.  The number 7 identifies the correct number to replace the ?.

[Gregory Matthews]

Hint:  Take the numbers in the list and subtract the number 72 from the number 99,  and examine the number that results.  If you find it to be meaningful, you should now know what to do next.  Continue on.  What is your conclusion?

 

[Gregory Matthews]

Hint #2: The numbers 99 and 72 are very important and key to solving the riddle.  In hint #1, I asked you to subtract one of the numbers from the other number.  That hint seemed in the beginning to lead you in the correct direction.  However, it was found to be false when you came to the number 7.  This time, instead of subtracting one number from the other, try adding the same numbers that I gave you in hint #!.  If you do it correctly, you will find a result that is meaningful.  If you do not do it correctly, you will obtain a number that you will find is not meaningful.  Can you correctly add the various numbers that I asked you to work with?  Remember, the math skills required to do it correctly are not above the math skills of an 8th grade student.

[Gregory Matthews]

NOTE:  Be careful to do exactly what I told you to do and not what you think I told you to do.

[Gregory Matthews]

Alright, here is the solution, as well as the incorrect one:

*  In the incorrect one, you subtract 72 from 99 and get 27 as an answer.  That looks like it works until you get to the end.

*  In the correct one, you add: 9 + 9 +7 +2 and you also get the number 27.  So now you go to the missing number and you add the digits for 36 and 21: 3 + 6 +2+ 1, which results in the number 12.

* Replace the ? with the number 12 and you end up with the end number of 7.

Like I said: It is so simple that an 8th grade student could do the addition and subtraction required to answer the problem.  You simply need to think out of the box.