**Each month, a new set of puzzles will be posted. Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.**

## MIND-Xpander Logic Problem

In basic algebra, a rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials. Reduce the following rational expression to its lowest terms (?).

## X-Sums Puzzles

The 4 numbers, in italics, outside the 9 circles represent the sum of the numbers in the 5 surrounding circles. The numbers in the circles can only be 1 to 9 and each number can be used only once. Four numbers have been provided to get you started. Find the number (?) that should be in the centre of the X.

## EQUATE+3 Puzzle

Each row, column & diagonal is an equation and you use the numbers 1 to 9 to complete the equations. Each number can be used only once. ‘Three’ numbers have been provided to get you started. Find the remaining six numbers that satisfies all the resulting equations. Note – multiplication (x) & division (/) are performed before addition (+) and subtraction (-).

## Feedback

There are more than one way of doing these puzzles and may well be more than one answer. Please let me and others know what alternatives you find by commenting below. We also welcome general comments on the subject and any feedback you'd like to give.

If you have a question that needs a response from me or you would like to contact me privately, please use the contact form.

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### Solutions

**MIND-Xpander** Logic Problem

**X-Sums** Puzzles

**EQUATE+3 **Puzzle

is the first xsums puzzle wrong in this month’s challenge?

I’ve checked both again (the 1st and 2nd x-sum puzzles) and I’ve found no errors in either…not sure what you referring to as being wrong? Please use the contact form to let me know what problem you are having?

Hi Gordon, Thanks for getting back to me. I was able to solve the second one, but let me expand on the first one that maybe I am not seeing properly. If I label the missing circles starting at the bottom left and going up diagonally as A,B,C,D,E. A+B+C+3+4 equals 31 when looking at the sum on the bottom so A,B,C must be a combination of 7,8 and 9. But when looking at the sum on the left of 25 A,B and C must still be a combination of 7,8 and 9. my problem is 24 plus 2 plus 1 equals 27 and not 25. so based on the bottom sum A + B + C = 24 and based on the left sum A + B + C = 22. Thanks for the puzzles and please let me know if I am missing something.

Hi Rodrigo, Thank you for bringing this to my attention. No, you are not missing anything. There is an error in the 1st X-sum puzzle. Your observation and conclusion is 100% correct. I reviewed the solution page last night where the values are correct but missed the error on the puzzle page. The 3 provided in the puzzle should have been a 5 which would then have given the correct results. Sorry for the confusion; thanks again for bringing this to my attention and well done for spotting it – much obliged. Please keep challenging yourself with the puzzles yet to come.

Hi Gordon, Thanks for taking the time to review my comments. I know you must have been inundated with phone calls and comments with the sums problem that I saw on yahoo.com that went viral where someone replaced a value from one of your puzzles. Thanks again for the puzzles that you provide and have a great day!