Show HN: How to mentally calculate the day of the week for any date

80 points by yang140 a day ago on hackernews | 24 comments
PART 1

The skill you're about to steal โšก

Some people can hear any date and name its weekday in about two seconds. No calendar. No counting from today.

Not memorization, not magic: two secrets + a little practice. By the bottom of this page, this is you. (Suspicious? Check those dates against a real calendar.)

PART 2

Secret #1: The Clock of Days ๐Ÿ•

Weekdays aren't a list โ€” they're a circle of 7. You know remainders from school; here's what they're for. Three challenges โ€” answer before the clock moves.

PART 3

Secret #2: The Secret Squad ๐Ÿ“…

All of , with a squad of dates already marked in gold. They share one spooky property โ€” spot-check any of them by tapping the calendar yourself.

The doubles

"9-to-5 at the 7-11"

The oddballs

Secret #2: one weekday owns the whole squad. Its name: the year's Doomsday โ€” coined by John Conway, who published this method in 1973 (Doomsday rule on Wikipedia โ†—).

Remember it in two lines: the doubles (4/4 ยท 6/6 ยท 8/8 ยท 10/10 ยท 12/12) + "I work 9-to-5 at the 7-11" (9/5 ยท 5/9 ยท 7/11 ยท 11/7). Then three odd ones: ฯ€-day 3/14 ๐Ÿ›ž, the last day of February, and Jan 3 (Jan 4 in a leap year โ€” February borrows the day, so January shifts).

Provable with your clock: โ€” every gap a perfect stack of weeks. The squad must march together. Every year. Forever.

PART 4

Your first real trick: any date this year ๐ŸŽฏ

The trick = nearest squad date โ†’ leftover โ†’ walk from the Doomsday. One together first.

PART 5

Time travel: what day were YOU born? ๐ŸŽ‚

One more fact โ€” you already own it: 365 รท 7 leaves remainder 1. So each New Year the Doomsday slides +1 โ€” and +2 when the new year has a Feb 29:

๐Ÿš€ The Time Machine

Enter any year โ€” the slide rule does the rest.

๐Ÿฅ‹ Black-belt: jump straight to ANY year โ€” no stepping (Conway's dozens trick)

Slides are +1 per year, +1 extra per leap โ€” but stepping 26 times is slow. Why dozens? 12 slides + 3 leap extras = 15 โ€” and 15 on a clock of 7 is just +1. One dozen = one slide.

Try any year: 2026 (drag the number)

For 19-something years the same steps work โ€” just start from Wednesday, 1900's Doomsday, instead of Tuesday.

PART 6

Perform it! ๐ŸŽฉ

Time to train like a stage wizard. Three rounds โ€” the helpers disappear as you level up.

๐ŸŽฉ Who to thank for this trick: John Conway invented the Doomsday Rule โ†— in 1973 and trained by making his computer quiz him at every login โ€” until any date took ~2 seconds. Stage mathemagicians still perform it. Now you can too.

1. The Leftover Trick ๐Ÿ•

Draw the 7-day circle and jump around it.

Say: "Add 700 days to a Tuesday? Still Tuesday! Only the leftover after throwing away 7s matters."

2. The Secret Squad ๐Ÿ“…

Show 4/4, 6/6, 8/8, 10/10, 12/12 in any calendar โ€” then Jan 3 and ฯ€-day.

Say: "Check them โ€” all the SAME weekday. And 9-to-5 at the 7-11 too. Every year has a Doomsday!"

3. The Yearly Slide ๐ŸŽ‚

Explain why calendars shift.

Say: "365 days = 52 weeks + 1 leftover. That's why your birthday moves one weekday every year โ€” two after a leap!"

4. The Performance ๐ŸŽฉ

Have someone pick a date; think out loud afterwards.

Say: "Nearest squad dateโ€ฆ count the leftoverโ€ฆ walk from the Doomsday. Ask me another!"

Stumped somebody with it? Claim your title: