The odd + 11 shortcut

The odd + 11 shortcut

Everything you have learned so far still stands. This page changes exactly one step of the method — the arithmetic that turns a year into its doomsday — and leaves the century anchor, the doomsday dates, the leap-year rule and the final count exactly as they are.

The standard route asks you to divide by 12, keep the remainder, divide that by 4, and add three numbers to the anchor. It works, but you have to hold three partial results in your head at once while you do it, and most people find that the part that falls apart under time pressure.

Odd + 11, published by Chamberlain Fong and Michael Walters in 2010, gets to the same answer while only ever carrying one number.

The four moves

1. Take the last two digits of the year. If that number is odd, add 11.
2. Halve it. It always divides evenly — that is the entire reason for the +11 in step one.
3. If that result is odd, add 11 again.
4. Take what is left from seven: 7 − (n mod 7). That is the year’s code — add it to the century anchor.

Worked example: 1966

The same year the standard route works through, so you can put the two side by side.

The 1900s anchor on Wednesday, which is 3. Hold that.

The last two digits are 66. That is even, so there is nothing to add — it stays 66.

Halve it: 66 ÷ 2 = 33.

33 is odd, so add 11: 44.

Now the last move. 44 mod 7 is 2, and 7 − 2 = 5. That is 1966’s year code.

Add it to the anchor: 3 + 5 = 8, and 8 mod 7 = 1 — Monday. Which is exactly what the divide-by-12 route gives for 1966. It has to be: these are two ways of writing the same calculation, not two different calendars.

A few more years, worked out

The one mistake everybody makes

Step four is 7 − (n mod 7), not n mod 7. Forget to subtract and you will get a confidently wrong weekday every single time, with nothing about the calculation feeling off. If your answers are consistently out by the same amount, this is almost always why.

Which one should you use?

Whichever sticks. They take a similar number of seconds once practised; the difference is what they ask of your memory. Divide-by-12 asks you to hold three numbers and add them at the end. Odd+11 asks you to transform one number four times. People who lose the thread on the first tend to like the second, and the other way round.

You can switch at any time and the rest of the site follows you — the hints while you play, the step-by-step after a miss, and which drills the practice roadmap shows you.

If you would rather go back to the standard arithmetic, that is Calculating a year’s doomsday.