# Happy Diwali!

One of the greatest joys during the Diwali Festival is to share sweets among friends. Ma went to the sweet shop and bought imartis, laddoos, and balushahis. She also brought along a large number of empty boxes.

"Count the number of sweets," she told me. I counted 210 laddoos, 252 imartis, and 294 balushahis.

"Okay, now let's see how good you are at mathematics," Ma said. "Your task is to pack the sweets equally in the boxes so that no sweet is left over," Ma said. I did not understand what she meant.

She explained that if I put "x" laddoos, "y" imartis, and "z" balushahis in the first box, then the other boxes should also contain x" laddoos, "y" imartis, and "z" balushahis. Not a single sweet should be left over.

"That's easy," I said. "I will pack two boxes, and each will have 105 laddoos, 126 imartis, and 147 balushahis. Both packets will have the same number of sweets, and no sweets will be left over.

Ma looked at me as if I were nuts. "Do we have only two neighbours?" she asked. "And, besides, can one family eat so many sweets? It will give them a bad tummy."

Ma said I must try to get the maximum number of boxes possible. "We have many friends; we must distribute sweets among all of them," she said.

I had thought it would be an easy task, but, now, I am stuck. Can you help me get the maximum number of boxes packed? What is the highest number of boxes that I can get?

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• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in