Number Play
Playing with digits
Play with digits and count how many numbers have each number of digits.
How many numbers have each number of digits?
| Digits | From | To | How many |
|---|---|---|---|
| 1 | 1 | 9 | 9 |
| 2 | 10 | 99 | 90 |
| 3 | 100 | 999 | 900 |
| 4 | 1000 | 9999 | 9000 |
| 5 | 10,000 | 99,999 | 90,000 |
Komal adds up the digits of numbers. This is the digit sum. For 68 it is 6 + 8 = 14. For 176 it is 1 + 7 + 6 = 14, and for 545 it is 5 + 4 + 5 = 14. Different numbers can have the same digit sum.
The smallest number with digit sum 14? One digit is not enough: the biggest digit is 9. With two digits, keep the tens digit as small as possible by making the units digit as big as possible: 9. Then the tens digit is 14 − 9 = 5, giving 59. The largest 5-digit number with digit sum 14? Make the first digit as big as possible, 9, then 5, then zeros: 95,000.
Dinesh wonders how many times he writes the digit 7 from 1 to 100. Count place by place:
- units place: 7, 17, 27, …, 97: 10 times;
- tens place: 70, 71, …, 79: another 10 times.
So he writes 7 20 times. (77 has two 7s, and we counted both: once in each list.)
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