## Solution to Puzzle #68: Number at the Intersection

The response to this puzzle was overwhelming…got many correct answers. First one to respond with the right answer was Anavi Baddepudi from Singapore – well done. Many others got correct answers – Pratik Sarkar, Vivek Shah, Ramendra Mandal, Anubhav Garg, Ravi Kuppanna, Shruti Sancheti and Rhea Mittal. Finally, happy to see that my elder one, Anisha Goyal, solved it as well!

Some people solved this puzzle the brute force way, i.e. they came up with a distribution of numbers in the boxes that satisfied the two conditions – horizontal row summing to 30 and vertical column summing to 22. An easier and cleaner way to solve for x is the following:

If you add the horizontal row and the vertical column, the number x gets added twice, and all the other numbers get added only once. Since digits 1…9 when added yield 45, this sum should be 45+x, which is also 30+22, which is already given to us. Solving gives us x as ‘7’.

Hope you enjoyed the puzzle!

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