juantheron
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How many of the first 
positive Integers has distinct Digits.
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SpiralFlex
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Where do you get your questions from? They are nice.
Three cases, 1 digit, 2 digits, 3 digits:
[Case 1]: 0,1,2,3,4,5,6,7,8,9
So we could use ONLY 9 out of 10 digits to fill the first box. For the second box digits except the one we have chosen to fit the first box. Hence there are 9 digits we can choose. Hence there are 9*9 distinct digits for 2 digit numbers.
[Case 2]:0,1,2,3,4,5,6,7,8,9
By similar fashion, 9 digits for the first one and second one but only 8 for the third.
[Case 3]: 0,1,2,3,4,5,6,7,8,9
Any of these could be used except 0 again since it isn't positive. There are 9 of them.
Summing it up, 9+9*9+9*9*8=738
Three cases, 1 digit, 2 digits, 3 digits:
[Case 1]: 0,1,2,3,4,5,6,7,8,9
So we could use ONLY 9 out of 10 digits to fill the first box. For the second box digits except the one we have chosen to fit the first box. Hence there are 9 digits we can choose. Hence there are 9*9 distinct digits for 2 digit numbers.
[Case 2]:0,1,2,3,4,5,6,7,8,9
By similar fashion, 9 digits for the first one and second one but only 8 for the third.
[Case 3]: 0,1,2,3,4,5,6,7,8,9
Any of these could be used except 0 again since it isn't positive. There are 9 of them.
Summing it up, 9+9*9+9*9*8=738
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So we could use ONLY 9 out ofa 10 figures to complete the first box. For the second box figures except the one we have selected to fit the first box. Hence there are 9 figures we can select. Hence there are 9*9 unique figures for 2 number figures.