The third challenge – number spellings

Hello everyone … we hope you will enjoy working on the problem below from the UK and Kenya! Please post your comments below.

First think of an integer written out in letters e.g. sixteen.

Take the number of letters in this number e.g. 7

Write this number out e.g. seven

Take the number of letters in this number e.g. 5

Write this number out e.g. five

Take the number of letters in this number e.g. 4

Write this number out e.g. four

Now we have converged to the number four.

Try this process with other numbers and see what happens.

Is it the same in other languages?

You may want to use the power of Python programming language to explore this further. You can make the Trinket below fullscreen by clicking on the three parallel lines in the top left corner and then clicking fullscreen (and do this again to stop it being fullscreen).

What day of the week …

… will the 28th of July 2061 be?  (Next predicted sighting of Halley’s comet)

… was the 4th of April 1965? (Robert Downey Jr ‘s birth)

… was the 17th of July 1789? (Prise de la Bastille)

We puzzled over these two questions having to think about where to start, the number of days in each month, and the rules for leap years.

It was fun to try different strategies by hand, but then we used the mod function and the floor function in Zeller’s algorithm to find quickly the day of the week for any date.

days of the week