o Example 1.1.6
•1) Find the number of positive integers containing 1 less than 10000
•2) Find the number of positive integers containing 0 less than 10000
1) Positive integers less than 10000 without 1 can be regarded as 4 digits, except 0000. Therefore, there are 9×9×9×9-1=6560.
Including 1: 9999－6560=3439
In addition: there are 10^4 all 4-digit numbers, 9^4 four-digit numbers without 1, and the difference of two 4-digit numbers with 1: 10^4 -9^4 = 3439.
2) There are 9 1-digit numbers without 0, 9^2 2-digit numbers, 9^3 3-digit numbers, and 9^4 4-digit numbers, so positive integers less than 10000 without 0 are
9+9^2 +9^3 +9^4 =(95-1)/(9-1)=7380;
Positive integers including 0 and less than 10000 are: 9999－7380=2619
Note: "Include 0" and "Include 1" cannot be directly applied. 0019 contains 1 but not 0. There are many similar implicit provisions in the combined exercises, and special attention should be paid to them.
let c1 = 0
let c0 = 0
for (let i = 1; i < 10000; i++) {
String(i).includes('0') ? c0++ : c0
String(i).includes('1') ? c1++ : c1
}
console.log(c0, c1)
2619 3439