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

« *Last Edit: March 05, 2004, 11:37:50 pm by BWJM* »

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**BWJM**, F.O.N.A.

Life Member of CPMS, RCNA, ONA, ANA, IBNS, WCS.

President, IBNS Ontario Chapter.

Treasurer, Waterloo Coin Society.

Show Chair, Cambridge Coin Show.

Fellow of the Ontario Numismatic Association.