Each week, students were presented with a puzzle to solve. These tasks were usually wrapped in some form of a story, given so much to conceal as informing, but the essence was the mathematical in nature. But offered the most satisfying tasks a logical shortcut that allowed one to reach the right conclusion without resorting to algebra, geometry or quadratic equations. The example of water lily and Lily Pond will illustrate their equally fascinating blend of simplicity and complexity frustrating:

The Squire had recently built a lily pond in Manor House, which was 15 feet long and eight meters wide. He ordered his gardener to plant a water lily in one corner of the pond. The selected water lily was a newly introduced brand known for its rapid growth. In fact, water lily growing at such a vast rate that the surface of the pond covered doubled each day. Seven days after it was planted, the water lily, covering half the surface of the lily pond. How long will it take before the pond was completely covered?

It is immediately obvious and wrong answer, which is fourteen days. There is also a long mathematical approach, which involves calculating the area of the dam and thus the speed of growth of water lily, which eventually provides the correct answer. Much more satisfying is the logical approach, which quickly discerns that the dimensions of the dam are as immaterial as the water lily was planted by the gardener or the Squire himself.

If none of the students came to the correct answer within the thirty-minute lesson, we were left to puzzle before next week when the answer was revealed. In the same spirit, instead of just revealing the solution for those who did’t reach it immediately, I’ll leave you with a little thinking time. After all, it’s nothing as satisfying as working on a puzzle at the moment when, quite unexpectedly, the light dawns.

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