Math Puzzles *UPDATED*

[Whitecloak]

Number of possible 3 digit numbers with 3 different digits = 9*9*8
Number of possible 4 digit numbers with 3 different digits = 9*9*8*4
Number of possible 4 digit numbers with 4 different digits = 9*9*8*7
Total numbers with more than 2 diff digits = 7776
Total numbers with less than or equal 2 diff digits = 9999 -7776= 2223

 

[Vertimus]

Originally posted by: whitecloak

Number of possible 3 digit numbers with 3 different digits = 9*9*8
Number of possible 4 digit numbers with 3 different digits = 9*9*8*4
Number of possible 4 digit numbers with 4 different digits = 9*9*8*7
Total numbers with more than 2 diff digits = 7776
Total numbers with less than or equal 2 diff digits = 9999 -7776= 2223

You can't assume the first digit is always a 0.

 

[sao123]

I believe the answer to #11 is 929.

0-99
(10 choose 1)*(10 choose 1) = 100

100-999
(9 choose 1)(9 choose 1)(2 choose 1) + (9 choose 1)*(1 choose 1)*(10 choose 1) = 252

1000-9999
(9 choose 1)*(1 choose 1)*(1 choose 1)*(10 choose 1) +
(9 choose 1)*(1 choose 1)*(9 choose 1)*(2 choose 1) +
(9 choose 1)*(9 choose 1)*(2 choose 1)*(2 choose 1) = 576

10000 = 1

EDIT: Common values for math
(10 choose 1) = 10
(9 choose 1) = 9
(2 choose 1) = 2
(1 choose 1) = 1
100 + 252 + 576 + 1 = 929

 

[Vertimus]

Originally posted by: sao123
I believe the answer to #11 is 929.

0-99
(10 choose 1)*(10 choose 1) = 100

100-999
(9 choose 1)(9 choose 1)(2 choose 1) + (9 choose 1)*(1 choose 1)*(10 choose 1) = 252

1000-9999
(9 choose 1)*(1 choose 1)*(1 choose 1)*(10 choose 1) +
(9 choose 1)*(1 choose 1)*(9 choose 1)*(2 choose 1) +
(9 choose 1)*(9 choose 1)*(2 choose 1)*(2 choose 1) = 576

10000 = 1

EDIT: Common values for math
(10 choose 1) = 10
(9 choose 1) = 9
(2 choose 1) = 2
(1 choose 1) = 1
100 + 252 + 576 + 1 = 929

The original question was "How many positive integers less than 10,000 have at most two different digits?". The correct answer is 927, which is the same as yours if you take off 0 and 10,000, so I'll give you credit for that.

Good job :thumbsup:

 

[sao123]

yay

 

[Vertimus]

Added more problems!

 

[JujuFish]

12) 14 total
9 multiples of 11
4 multiples of 12
15

 

[MrDudeMan]

damn it jujufish, i had the answer too. :|