When I microwave, I don’t press 1, 0, and 0 to set a one-minute timer. Instead, I press 6 and 0. This way, I can save a third of the energy used every time I microwave food for some time of less than or equal to 1 minute and 39 seconds. But the calculation doesn’t end here. There must be a way to determine the best sequence for entering a time on the microwave keypad.

Now, to determine the best sequence we have to calculate the distance between each button. First, we can convert the microwave keypad into a coordinate system:

The button 1 is positioned at (-1, 3).

The button 2 is positioned at (0, 3).

The button 3 is positioned at (1, 3).

The button 4 is positioned at (-1, 2).

The button 5 is positioned at (0, 2).

The button 6 is positioned at (1, 2).

The button 7 is positioned at (-1, 1).

The button 8 is positioned at (0, 1).

The button 9 is positioned at (1, 1).

The button 0 is positioned at (0, 0).

Next, to calculate the minimum distance, we can use the Euclidean distance formula:

The total distance for a sequence would be calculated as the sum of individual differences. Next, when determining the optimized sequence for entering a specific time, there might be multiple ways to input the sequence. If the seconds component is less or equal to 39, there are potentially two options to represent the time:

Entering the time as MMSS, where M represents the minutes and S represents the seconds. Adjusting the sequence so that the total seconds fit within a single minute, which can be written as (MM-1)(SS+60).

For example, when computing 2 minutes and 39 seconds, the valid sequences are “239” and “199”.

If we calculate the distance travelled, “239” would yield a result of 3.0 units whereas “199” would yield a result of approximately 2.8284 units. This effectively saves about 5.7% of the original energy required.

Another example would include computing 5 minutes and 31 seconds, which has valid sequences “531” and “491”.

The sequence “531” has a distance of around 3.41 while the sequence “491” has a distance of around 5.06. That’s about 32.6% of the energy saved!

The algorithm has spoken!