**From New Scientist #2868, 9th June 2012** [link]

The display on my calculator shows 9876543210.

As usual, up to seven illuminated strips are used to display each digit – the 8 using all seven, for example. There is just one special 10-figure number with the property that it is a perfect power of the total number of illuminated strips that it uses.

With a little calculator effort it is possible to answer the following: How many illuminated strips does this special 10-figure number use?

[enigma1701]

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The following Python program runs in 38ms.

In order to get a solution I have to assume a 3-segment “7” (rather than the 4-segment “7” that my old Casio calculator actually displays). Choosing 5-segment “6” and “9” digits (rather than the more usual 6-segment display) does not affect the solution.

Solution:The number illuminates 41 segments of the display.I was puzzled as to why I wasn’t getting any solution with a 4-segment 7.

I get the same result: one solution with a 3-segment 7, no solution with 4-segment 7.

Now I have my paper copy of the magazine there is a diagram showing the digits, and it makes clear that a 3-segment “7” is used (and 6-segment “6” and “9”). I have updated the question to the show the arrangement of the digits.

Ah, that explains it. I was wondering whether the original specified the display.

Looking at numbers with fewer than ten digits I found

130691232 = 42^5

1336336 = 34^4, 1500625 = 35^4, 2560000 = 40^4.

These don’t depend on a three-segment 7 (normal for clocks but not calculators, for reasons that are lost on me). I’ve never heard them called “illuminated strips”!

Here is mine: