The Tiffin Swap Game

The story

It was a typical Friday at school when Kabir and Riya's tiffins got mixed up. Their group of five friends stared at a pile of lunchboxes, all now in the wrong hands. Kabir felt sure his, with the blue tape, would never get swapped. Riya believed each tiffin looked different enough to avoid confusion. When the bell rang, everyone hurriedly picked a tiffin. Kabir ended up with lemon rice instead of his usual parathas. Wondering how many possible mix-ups there could be, Kabir guessed it couldn't be many, while Riya estimated just a handful. On a call, their Aaji explained it was more than they thought. She began counting: five possible tiffins for the first friend, then four left, then three, two, one. How many could that be?

The science

This lunchtime mix-up is an example of a permutation, where we count how many ways different items can be ordered. For five tiffins, the first person can pick from all five, the second picks from the four remaining, and so on. Mathematically, this order is 5 times 4 times 3 times 2 times 1, which equals 120. So, there are 120 possible ways for the five tiffins to get swapped among five friends. Every different order counts as a unique arrangement.

Try it

Questions students ask