Popular Misconceptions

This mathematical equation appeared within the ‘list of facts’ e-mail I received a while back. Whilst many of the others have so far turned out to be popular misconceptions, this one is demonstrably true (it would have been fairly foolish to get it wrong!).

Whilst it might initially seem surprising that 111,111,111 x 111,111,111 = 12,345,678,987,654,321 - perhaps you might even wonder how such a mathematical oddity could exist - when you stop and think about it, the equation is less of a co-incidence than you might think.

Let’s look at the sequence of squaring ever longer strings of 1s:

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12,321

1,111 x 1,111 = 1,234, 321

You can guess the rest…

Why should this be? Well it’s easier to see if you do the maths the high school way:

  111   x
  111
-----
  111
 111
111
=====
12321

Does that take the mystery out of it?

If you try 1,111,111,111² then the pattern is slightly messed up, as the middle number is forced to carry (although most calculators won’t show this, so you’ll have to do it on paper). However, if you want to try using base 11 or higher…

One of the items in a ‘list of facts’ e-mail I received a while ago contained this lesser-known claim to the history of the four suited kings in a pack of standard playing cards:

Each king in a deck of playing cards represents a great king in history:
Spades - King David
Hearts - Charlemagne
Clubs - Alexander, the Great
Diamonds - Julius Caesar

As usual, I’ve trawled the internet for existing refutations or confirmations of this supposed truth. It didn’t take too long to realise that the history of playing cards is pretty complicated, and disputed. Probably the best introduction to this subject comes from a essay titled The Introduction of Playing-Cards to Europe, which warns:

The history of playing-cards in Europe has been subject to a good deal of misinformation. You should evaluate all information about this subject cautiously because of this.

That essay, and the Wikipedia entry on Playing Cards, date the origin of playing cards to the 9th Century, in China. Whilst China is fairly geographically opposite from the domains of the kings listed above, playing cards clearly went on to circumvent the globe, getting adapted and changed along the way.

Even though we know that the original origin of the kings on playing cards cannot have represented David, Charlemagne, Alexandar and Ceasar, that doesn’t rule out the possibility of their identities having been assigned later. Looking into it, it’s not too hard to find scans of old cards with the four king’s names printed on them - see the Courts on Playing Cards webpage, for example.

The Wikipedia page on King (playing card) suggests that the David, Charlemagne, Alexandar and Ceasar King combo were the traditionally-assigned personalities for the ‘French deck’, which was subsequently adopted in the UK due to the manufacture of playing cards being illegal in the UK during the Interregnum.

This explanation is the same as the one given on the Snopes.com page on The Four King Truth. On their comprehensive page (last updated 7 February 1999), they summarise that:

The assignation of identities to the kings (as well as the queens and knaves) was a temporary practice unique to French card masters that began around the mid-15th century, was not standardized for some time, and was discontinued at the end of the 18th century.

In conclusion, the Snopes article states that the ‘four kings truth’ is false, and that ‘the royal figures on modern playing cards no more represent specific persons than do the kings and queens in chess sets’.

That falsification didn’t seem quite so strong to me. Whilst the kings, queens and jacks in the picture cards don’t seem to have arisen with any particular historic figures in mind (clearly they’re there for the sake of the game rather than purely for symbolic reference), the connection with kings David, Charlemagne, Alexandar and Ceasar does seem to genuinely go back at least some way.

So perhaps it’s half true then?