Radar Note Frequencies

News: Welcome to the Canadian Paper Money Forum.

I had the pleasure of a great conversation with Mike_L the other day and he showed me a rather interesting note.  It involved digits that when the entire number was rotated 180 degrees, it looked like the same number.  I asked him how many of those were there and we figured it out.  Then I wanted to figure out the number of radar notes per run of 10 million notes.

Here's our results:
4-digit radars: 10x9x8x7 = 5040
3-digit radars: 10x9x8x6 = 4320
2-digit radars: 10x9x7   =  630
Solid radars:   10-1^*    =   9
Total radars and solids:   9999

So, one can see why 3- and 4-digit radars are clumped together in the Charlton guide... They account for 9360 of the possible 9999.

Now, here's what sparked this conversation...  Mike showed me a note with a number like 9908066.  Notice that if you rotate that whole number around by 180 degrees, it looks exactly like it did before, but the note would obviously be upside-down and the prefix wouldn't be in the right place.  I thought that was really cool.

This can only be achieved using {0, 6, 8, 9} for the first three digits and {0, 8} for the centre digit, then the corresponding "flipped" digit in the right spot of the last 3 digits.  By "flipped", I mean that 0->0, 6->9, 8->8 and 9->6.  You can't use 1s because of a little "tick" at the top of them that makes them non-symmetrical.  Using this information, we figured out that there are only 127 (4x4x4x2-1)^* possible notes per run of 10,000,000 that would be "rotators" like the one Mike showed me.  That means that they're a little more common than solid radars and million-numbered notes, but more scarce than 2-digit radars!

^*Subtracting one because 0000000 is always removed and destroyed.

Some other examples of "rotators" are:
9098606
9860986 (also a repeater)
8888888 (also a solid radar)
6668999
0090600
6600099
8998668

bc_collect sent me a note a moment ago about BABN's practice of removing the entire SHEET that contains 0000000.  So, that effectively removes 9 more of the 2-digit radars (0001000, 2, 3, 4, 5, 6, 7, 8, 9).  The total 2-digit radars now drops to 621 and the grand total number of radars is 9990.

Thanks bc_collect!

But how many 2 digit repeater radars would there be in 10 million notes eg.  2424242---7575757?

But how many 2 digit repeater radars would there be in 10 million notes eg.  2424242---7575757?

That's an easy one:

There are nine that start with 0 (0101010, 0202020, 0303030, etc)
There are nine that start with 1 (1010101, 1212121, 1313131, etc)
etc...
etc...
There are nine that start with 9 (9090909, 9191919, 9292929, etc)

Ten times nine = ninety.  

bc_collect sent me a note a moment ago about BABN's practice of removing the entire SHEET that contains 0000000.  So, that effectively removes 9 more of the 2-digit radars (0001000, 2, 3, 4, 5, 6, 7, 8, 9).  The total 2-digit radars now drops to 621 and the grand total number of radars is 9990.Thanks bc_collect!

Does CBN remove the entire sheet as well?

That's a myth.

That's a myth.

I thought so too 

I know that the solid 0000000 is removed, but I kind of thought that the others were not......thereby assuming only the 0000000 note is removed once the sheet is cut into bricks...