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my answer is 56, although i am not happy about how i came to it..

#of 1 digit numbers: 1 For 2 digits we have (2,3),(4,1) #of 2 digit numbers: 4 + 1 (this one is derived from adding a 0 to the 1 digit number) = 5 For 3 digits we have (1,1,3)(1,2,2) #of 3 digit numbers: 3!/2!+3!/2!+ 1 (500) + 4*2 (adding one zero to the 2 digit numbers - 2 ways, in between or at the end) = 15 For 4 digits we have (1,1,1,2) #of 4 digit numbers: 4!/3! + 1 (5000) + 4*3 (adding 2 zeroes to the 2 digit numbers - 3 ways, in between, at the end, or one in between and one at the end) + 6*3 (adding one 0 to the 3 digit numbers - 3 ways, after 1st digit, after 2nd digit, after 3rd digit) = 35

positive integers less than 10,000 => the number has 4 digits

made of (5,0,0,0), (1,1,1,2), (4,1,0,0), (3,2,0,0),(3,1,1,0),(2,2,1,0)

(5,0,0,0) => 5000, 0500, 0050, 0005 => 4 Similar to (1,1,1,2) =>4

(4,1,0,0): as 1,4 can be interchangable 4100 4010 4001 0410 0401 0041 => 6 * 2 = 12 Similar to (3,2,0,0) => 12 Similar to (3,1,1,0) => 12 Similar to (2,2,1,0) => 12

I got this one also after like 6 minutes. My response would simply be this... if you were to see something this difficult on the test... just take a wild guess since you already are in the 99% rofl
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