## Introduction: John Conway Doomsday Device

John Conway is a legendary mathematician who among his many achievements, devised a simple algorithm for figuring out in your head on what day of the week any calendar date would fall. He called it the Doomsday Rule. He was known to be able to perform this mental calculation in under 2 seconds. The same steps in the calculation can also be carried out using a simple device made out of paper and cardboard.

I call it a Doomsday Device

## Supplies

• A sheet of A4/letter sized paper
• Inkjet or laser printer
• Cardboard - doesn't have to be blank. You can use recycled food packaging
• Glue

## Step 1: Print Out the Doomsday Discs

The John Conway Doomsday Device consists of 7 circular discs of varying radii. Print them out on a single sheet of A4 or letter sized paper.

## Step 2: Attach Cardboard Backing and Cut Out Discs

1. Glue a cardboard backing to the print out. When applying the glue make sure you have completely coated the backs of discs A, B, C, D, E, and G. Do not apply any glue to disc F.
2. When the glue has dried cut out the discs. Disc F should be the only disc without a cardboard backing.

## Step 3: Cut Centre Hole, Slits, and Slots

1. Cut out the round hole in the centre of discs A, B, C, F and G.
2. Cut two short narrow slits on either side of the centre circle on discs D and E
3. Cut out the grey slots marked on discs A, B and D.

## Step 4: Create Central Shaft

1. Roll a short strip of cardboard, about 2 cm wide, into a cylinder. This cylinder should be small enough to pass through the central holes you've cut into discs A, B, C, F and G.
2. Cut four slits in the end of the cylinder, evenly spaced. Bend the tabs you've just created outwards, leaving a pair of tabs which should fit into the slits you have cut in disc D.
3. Glue disc D to the cylindrical shaft. Be careful not to use too much glue. The other discs need to be able to spin freely.

## Step 5: Assemble the Doomsday Discs

1. Assemble the other discs onto the cylindrical shaft in order: A, B, C
2. Discs F and G should be flipped to face the other way.
3. Cut four slits into the other end of the cylindrical shaft, bending the tabs outward but leaving two tabs which will fit into the slits in disc E.
4. Glue disc E to the cylindrical shaft.

## Step 6: Calibrate Your Device

You may notice that disc F rotates freely with respect to disc C. Your Doomsday Device needs to be calibrated.

1. Line up all the slots of discs A, B, and D with the number 2100.
2. Carefully flip your device over so as not to rotate any of the discs.
3. Rotate disc F to align with "Sunday" on disc E, while being careful not to move any of the other discs.
4. Now glue discs F and C together.

Your John Conway Doomsday Device is now complete.

## Step 7: How to Calculate the Day of the Week

In order to show you how to use your Doomsday Device to calculate the day of the week of any given date, let us first try a simple worked example:

22nd December 2134

1. Rotate the slotted discs to expose three numbers that add up to the year, 2134. That is, 2100 + 24 + 10. Other numbers might appear in two of the slots. They can be ignored.
2. Turn over your device. The indicator disc points to the Doomsday for that year - Sunday
3. Rotate the month disc so that the indicator points to the sector containing DEC
4. Now look for the date, 22. It is in the same sector as the day of the week for that date: Wedneday

So the 22nd of December 2134 falls on a Wednesday

## Step 8: Calculating the Day of the Week (Advanced Example)

Since the Gregorian calendar repeats on a 400 year cycle, you can still use the Doomsday Device for years such as 2276 by simply dialing the year 1876

12th of February 2276

1. Rotate the slotted discs to expose three numbers that add up to the year, 1876, 1800 + 72 + 4.
2. Turn over the device. The Doomsday for that year - Tuesday
3. Rotate the month disc so that the indicator points to the sector containing FEB. Notice that for the months, January and February, you have a choice of two different positions. The year 2276 is a leap year, so use the FEB that is highlighted in green.
4. Now look for the date, 12. It is in the same sector as the day of the week for that date: Saturday

Thus the 12th of February 2276 will fall on a Saturday.

Now try out your Doomsday Device with other dates. Try guessing the day of the week without using your device. If you practice enough, you might get to be as fast as John Conway!

Participated in the
Back to Basics Contest