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PUZZLET 192

UniDigits from 7-Segment Displays

This week's Puzzlet is all about 7-segment digital displays, named that way because every digit is formed from a combination of no more than seven segments.

digits

The display uses the following number of segments to make each digit, as illustrated in the diagram above:

Digit Displayed
1
2
3
4
5
6
7
8
9
0
Nr of Segments
2
5
5
4
5
6
3
7
6
6

A product-counter has three 7-segment digits, initially set at 000. The  number of segments addressed is thus 3 x 6 = 18. The first product increments the display to 001, addressing only 14 segments this time. The total number of segments addressed so far is 18 + 14 = 32. The next display will be 002, giving a total number of segments addressed of 49. A series of these totals results, generating 18, 32, 49, 66, 82 . . .

The fourth term is UniDigit 66 (all digits the same).  Find all UniDigits generated this way for a count of 50,000 products.

Note that the product counter rolls over to zero after it reaches 999.


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Last Updated:  January 17th, 2010.