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◻➕◻➕◻➕◻➕◻=30 Fill the boxes using (1, 3, 5, 7, 9, 11, 13, 15) U can also repeat the numbers..This question came in UPSC Final Exams held in Dec '13...... You will be glad to note that only Vivek Singh could solve it.

This question is wrong, and I can prove it too. There are boxes, and every one to be filled with odd number. every odd number is of the form :- 2a+1 2b+1 2c+1 2d+1 2e+1 2f+1 2g+1 2h+1 2i+1

I have taken 9 cases because your question has 9 boxes. Now on adding all of them, we get 2 (a+b+c+d+e+f+g+h+i) + 9 = 2(a+b+c+d+e+f+g+h+i+4) + 1 Hence proved, that it will always yield an odd number.

every odd number is of the form :-

2a+1

2b+1

2c+1

2d+1

2e+1

2f+1

2g+1

2h+1

2i+1

I have taken 9 cases because your question has 9 boxes.

Now on adding all of them, we get 2 (a+b+c+d+e+f+g+h+i) + 9 = 2(a+b+c+d+e+f+g+h+i+4) + 1

Hence proved, that it will always yield an odd number.