What it shows
In any year the dates 4/4, 6/6, 8/8, 10/10, 12/12, 9/5, 5/9, 7/11, 11/7 and the last day of February all fall on the same weekday, called the doomsday. A wheel finds the doomsday for the year, and counting from the nearest of these dates gives the weekday of any date, such as 15 August 1947, a Friday.
The science
A normal year has 365 days, which is 52 weeks and 1 day, so the same date moves one weekday later each year, and two days after a leap year. The doomsday dates are chosen because they are exactly a whole number of weeks apart: 4/4, 6/6, 8/8, 10/10 and 12/12 are 61 days apart in pairs with a 63 day gap in the middle, and 61 + 63 patterns keep them on the same weekday. To find a year's doomsday, take the last two digits of the year, divide by 12, and add the quotient, the remainder and the remainder divided by 4, then count on from the century anchor: Tuesday for 2000 to 2099 and Wednesday for 1900 to 1999.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- Two card circles, 20 cm and 14 cm, joined at the centre with a split pin
- A marker and ruler
- A list of the doomsday dates printed on the base
- A calculator to check
- An old calendar for testing
Safety
For this project: An adult must push the split pin through the card.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Write the seven weekdays round the big circle, and the numbers 0 to 6 round the small circle, so turning the small circle lines up a count with a day.
Print the doomsday dates on the base: 4/4, 6/6, 8/8, 10/10, 12/12, 9/5, 5/9, 7/11, 11/7, 3 January in a normal year or 4 January in a leap year, and the last day of February.
Find the doomsday for 2026: 26 divided by 12 is 2 remainder 2, and 2 divided by 4 is 0, so 2 + 2 + 0 = 4. Set the wheel to Tuesday plus 4: Saturday.
Test it: 10 October 2026 is a Saturday, so 14 October 2026 is a Wednesday. Check against a calendar.
Find the weekday of 15 August 1947: 47 divided by 12 is 3 remainder 11, 11 divided by 4 is 2, total 16, which is 2 more than a multiple of 7. Wednesday plus 2 is Friday, so 8 August 1947 was a Friday and 15 August 1947, one week later, was also a Friday.
Let visitors call out their birthdays and find the weekday on the wheel, then check on a phone.
Make a card explaining the leap year rule: every 4 years, except century years not divisible by 400, so 2000 was a leap year and 1900 was not.
Mount the wheel with a worked example beside it and a list of century anchors: 1800s Friday, 1900s Wednesday, 2000s Tuesday, 2100s Sunday.
What you should see
The wheel gives Saturday as the 2026 doomsday and Friday for 15 August 1947, both correct against a calendar, and visitors' birthdays check out on a phone.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1Why does the same date move one weekday forward each year?
Because 365 days is 52 weeks plus 1 day.
2Why is 4/4 always on the same weekday as 6/6?
They are 63 days apart, exactly 9 weeks.
3Was 1900 a leap year?
No. Century years are leap years only if divisible by 400, so 2000 was but 1900 was not.
4What is the last doomsday date in February of a leap year?
29 February, the last day of the month.
Take it further
Work out the weekday of your 50th birthday and of 26 January 1950, and show both with the wheel.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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