Coding classes in Perth and Kinross

Zeller's congruence works on the day, the month and the year, split into its century and its last two digits. It adds a handful of whole-number quantities and takes the remainder after dividing by 7, which gives a number from 0 to 6: 0 for Saturday, 1 for Sunday and so on. There is one strange rule. January and February are treated as months 13 and 14 of the previous year, because the formula counts from March so that the awkward February leap day falls at the end. The learner codes it in a few lines of Python and asks it about 7 October 1847. The answer is Thursday, and Python's own date library agrees.

The first bug is the classic. Forget the January and February shift and the formula is wrong on every one of those days and right on all the others, so testing a handful of dates in summer never finds it. The second is subtler. A popular version of the formula subtracts twice the century instead of adding five times it, which is equivalent in mathematics but can make the total negative. Python's remainder of a negative number is still between 0 and 6; the remainder in C, Java and JavaScript keeps the minus sign. Port the formula from one language to another and it returns -6 for 2 March 1800 and is wrong on 2,285 days in three centuries, yet perfect on every date anyone thinks to try by hand.

Exhaustive testing catches both, and the learner can then ask playful questions with confidence. Over a full 400-year cycle of the Gregorian calendar, the 13th of the month falls on a Friday 688 times out of 4,800, slightly more often than on any other day. The cycle repeats exactly every 400 years, so that is a fact, not a sample.

Proving a program right, instead of hoping, is the reason Perth and Kinross teenagers should keep learning to code in 2026. The longer argument is in why teenagers should still learn to code in 2026.