How many positive integers between 1000 and 9999 inclusive are divisible by 7?

Are divisible by 7?

(1/7)9000 = 1286

Are even?

(1/2)9000 = 4500

Have distinct digits?

I don't know what that means. No repeated digits? Maybe 3024?

Are not divisible by 3?

(2/3)9000 = 6000

Are divisible by 3 or 4?

[(1/3) + (1/4) - (1/12)]9000 = (6/12)9000 = (1/2)9000 = 4500

Are not divisible by either 3 or 4?

9000 - 4500 = 4500

Are divisible by 3 but not by 4?

[(1/3) - (1/12)]9000 = (3/12)9000 = (1/4)9000 = 2250

Are divisible by 3 and 4?

(1/12)9000 = 750

function count(a, b, n){

b = Math.floor(b/n);

a = a%n==0 ? Math.floor(a/n)-1 : Math.floor(a/n);

return b-a;

}

function c(n){return count(1000,9999,n)}

7s = c(7) = 1286

evens = c(2) = 4500

not 3 = c(1)-c(3) = 6000

3s or 4s = c(3) + c(4) - c(12) = 4500

not = c(1) - (c(3) + c(4) - c(12)) = 4500

3 not 4 = c(3) - c(12) = 2250

3 and 4 = c(12) = 750

div. by 7 ... 1001 .... 9996

9996 = 1001 + 7(n-1)

7n - 7 = 8995

7n = 9002

n = 1286 ... 1286 pos. integers from 1000 to 9999 that are div. by 7

now you try the others