Giving students an insight into mathematical savants and other mathematical geniuses is a good way of invoking a sense of wonder about the subject. Calendar savants are able to correctly name the day of the week from any given date in history – almost instantly. Whilst it is still not clear how they do this, it is possible to achieve the same feat using a relatively straightforward algorithm. To make things easier, limit the prediction to the first decade of the 21st century.

**Step 1 – Memorise (or discreetly write it on the board somewhere) a twelve digit number: **622 – 503 – 514 – 624. Each digit corresponds to a month of the year. January is 6, February is 2, March is 2 etc etc.

**Step 2**** – ****Learn to work in mod 7. **In mod 7 we just look at the remainder when dividing by 7. 36 divided by 7 is 5 remainder 1. So 36 is 1 (mod 7). 23 divided by 7 is 3 remainder 2. So 24 is 2 (mod 7). A number like 14 would be 0 (mod 7).

Now we’re ready to start the calculation. This particular method will calculate the day of the week for any date in the 21^{st} century (it can be slightly adapted to calculate dates in previous centuries). The date for our example will be March 10 2004.

**Step 1 **– work out the day of the month mod 7. In this case 10 is 3 mod 7.

**Step 2 **– add the month value. The month value (from the preparation step) is 2. Therefore 3 + 2 = 5.** **

**Step 3 **– count how many years since 2000. This is 4 years in our example. Add the 4 to the 5 from the last step = 9. This is 2 (mod 7).

** Step 4 – **adjust for leap years. There was a leap year in 2000, then in 2004, then 2008 etc. So in our example there had occurred 2 leap years (if our date was before March 1^{st} then we wouldn’t count the 2004 leap year). Add this 2 onto the previous answer. 2 + 2 = 4.

**Step 5 –** The number you have left relates to the day of the week. Sunday = 1 Monday= 2, Tuesday = 3 etc. So March 10 2004 was a Wednesday (check below! Red dates are Sundays.)

You can check the calendars for the 21st century here.

**Lesson Plan:**

Learning objectives: This is a nice little activity that can be used either as a starter or as part of a larger lesson on mental arithmetic, or as part of a lesson looking at mathematical savants and other mathematical geniuses throughout history. The lesson resources are uploaded on TES here.

** 5 minutes:**

Watch video on autistic savants. Discuss about can this be possible? Highlight links between savant ability, high functioning autism mathematical geniuses.

** 5 minutes:**

Demonstration! Have a student choose any date from 1^{st} January 01 2000 to 31^{st} December 2009. Give all students a copy of the calendar sheets. Following the rules below correctly give the day of the week for that date. Try it one more time.

** 10 minutes: **

Discuss that this was done using an* algorithm* – a set of instructions to follow. And that students can also learn to do this. Hand out the sheet “How to Calculate like a Mathematical Savant.” Go through the rules – then let the students practice in pairs. Can they get it correct?

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