Larger numbers that can be formed by adding segments to displayed digits

Asked Mar 08 '17 at 16:31

Active Mar 08 '17 at 17:18

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The digits from 0-9 can form other digits by adding segments (as in an electronic display (7 segment display)). So:

From 0 you can form: 8;
From 1 you can form: 0,3,4,7,8,9;
From 2 you can form: 8;
From 3 you can form: 8,9;
From 4 you can form: 8,9;
From 5 you can form: 6,8,9;
From 6 you can form: 8;
From 7 you can form: 0,3,8,9;
From 8 you can form: -;
From 9 you can form: 8;

I have a number N of at least 2 digits and I need the number of numbers that can be formed with digits of N that are bigger than N.

Let's say N is 823. I take it's digits (8,2,3) and, with 8 i get nothing, with 2 i get 8 and with 3 i get 8,9. With this, i need the number of all the numbers i can get by combining these that are bigger than N. So 828, 829, 883, 888, 889. (5 numbers). Is there a formula for such a thing? Thank you in advance!

edited Mar 08 '17 at 17:18

Joffan

39,627

asked Mar 08 '17 at 16:31

Chor May

What do you mean when you say a number can be "formed with digits of N which are bigger than N"? – lioness99a Mar 08 '17 at 16:39
Well if N is 823, 828,829,883,888,889 are all bigger than N – Chor May Mar 08 '17 at 16:41
@Joffan yes, sorry for that! – Chor May Mar 08 '17 at 16:42
@Joffan just did! Thank you a lot for your comments – Chor May Mar 08 '17 at 16:46
@Joffan it can vary, it does not need to be 823 necessarily, and it can also be bigger than 3 digits , it can be 2 but never 1 digit only – Chor May Mar 08 '17 at 16:51
I think you will need to be more specific in the question. Do you maybe mean "which digits can be formed by adding one or more lit segments"? – mathreadler Mar 08 '17 at 17:05
If I understand your rules correctly, from $210$ you can get $218,230, 238,240,248,270,278,280,288,290,298,800,808,810,818,830,838,840,848,870,878,880,888,890$, and $898$. Did I miss anything, or include anything that doesn't belong? – Barry Cipra Mar 08 '17 at 17:15
@ChorMay Note update, please revert if this is not in line with what you meant. – Joffan Mar 08 '17 at 17:18
@BarryCipra yes, that is correct! I only need the number of elements if that makes it easier! – Chor May Mar 08 '17 at 17:23
@mathreadler exactly! – Chor May Mar 08 '17 at 17:23
@Joffan, I think your edit helps a lot. – Barry Cipra Mar 08 '17 at 17:24
@Joffan what you did is correct! Im sorry that it took a long time for you guys to understand me,im very bad at explaining what I want to happen! xD – Chor May Mar 08 '17 at 17:28
@ChorMay, asking clear, cogent questions is a nontrivial skill, but one that's well worth cultivating! – Barry Cipra Mar 08 '17 at 18:45
Adding comment in case this makes this question on the top of the question list again. I still need help with it – Chor May Mar 09 '17 at 18:36

Larger numbers that can be formed by adding segments to displayed digits

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