Odd + 11: A Faster Year Step for the Doomsday Algorithm

Most of the Doomsday algorithm is recall: the century anchors, the doomsday dates, the leap-year rule. There is only one part that is genuinely arithmetic — turning the year into a number you add to the century anchor — and it is the part that falls apart under time pressure. Odd + 11 is a different way to do that one step. If you have not met the method at all yet, start with what the Doomsday algorithm is.

What it replaces

Conway’s original year step asks you to take the last two digits of the year and work out three numbers: how many 12s fit into it, what is left over, and how many 4s fit into that leftover. Then you add all three to the century anchor and take the result modulo 7.

It is not difficult arithmetic. The difficulty is that you are holding three partial results in your head at once while still doing sums — and if you lose one of them, you start over.

Odd + 11, published by Chamberlain Fong and Michael K. Walters in 2010, reaches exactly the same number while only ever carrying one.

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 exactly — that is what the +11 was for.
3. If the result is odd, add 11 again.
4. Take what is left from seven: 7 − (n mod 7). Add that to the century anchor.

A worked example: 1966

The 1900s anchor day is Wednesday, which is 3. Hold that and forget the century.

• Last two digits: 66. Even, so nothing to add.
• Halve it: 66 ÷ 2 = 33.
• 33 is odd, so add 11: 44.
• 44 mod 7 is 2, so the year code is 7 − 2 = 5.

Anchor plus code: 3 + 5 = 8, and 8 mod 7 = 1 — Monday. So every doomsday date in 1966 (4/4, 6/6, 9/5, 7/11, and the rest) falls on a Monday, and any other 1966 date is a short count away from the nearest of them.

Conway’s route gives 3 + 5 + 6 + 1 = 15, and 15 mod 7 = 1. The same Monday, as it must be — these are two ways of writing one calculation, not two different calendars.

A few more, at a glance

The mistake to watch for

The last move is 7 − (n mod 7), not n mod 7. Stopping one step early gives you a confidently wrong weekday, with nothing about the working feeling off — and it is wrong for every date until you catch the habit. If your answers are consistently out by the same amount, this is almost always the reason.

Which one should you learn?

Whichever sticks. Practised, they take about the same time; what differs is what they ask of your working memory. Conway’s route asks you to hold three numbers and add them at the end. Odd + 11 asks you to transform one number four times. People who keep losing the thread on the first often get on much better with the second, and plenty of people find the opposite.

It is also worth saying that this changes one step. The century anchors, the doomsday dates, the leap-year shift in January and February, and the final count to your date are all identical either way — so switching costs you none of what you have already learned.

Try it

The odd + 11 lesson walks the method interactively, and there are two drills for it: Odd + 11 for the fold itself, and Year code (odd + 11) for the whole route against a clock. You can also set it as your preferred route in settings, and every hint and worked solution on the site will follow.