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How many times do you write 4 when you write the numbers from 400 to 600?
Wiki User
∙ 11y ago
We will have to count the same number multiple times (i.e., if a number has two fours, it will have to be counted twice). That is what makes this problem sort of tricky. Because the range is pretty small, we can solve it by just thinking it through in small cases:
Case 1: For the numbers: 400-499
- There are 100 digits that start with 4
- There are 10 digits that have a second digit of 4 (i.e., 440-449)
- There are 10 digits have that a last digit of 4 (404, 414, ... , 494)
(note: any type you are counting 0 to 9, you can assume 10 numbers, because the 0 counts as well)
The total number of four's in the interval [400,499] = 100+10+10 = 120
Case 2: For the numbers: 500-599
- There are 0 digits that start with 4
- There are 10 digits that have a second digit of 4 (540 - 549)
- There are 10 digits that have a last digit of 4 (504, 514, ... , 594)
The total number of four's in the interval [500,599] 10+10=20
There is not a third case. The only digit left is 600, and it obviously has no fours.
Therefore your answer is the sum of the two cases: 120 + 20 = 140
The numbers happen to be as follows (note: I've listed each number the number of times four appears, so for example 444 appears 3 times)
400, 401, 402, 403, 404, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 434, 435, 436, 437, 438, 439, 440, 440, 441, 441, 442, 442, 443, 443, 444, 444, 444, 445, 445, 446, 446, 447, 447, 448, 448, 449, 449, 450, 451, 452, 453, 454, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 494, 495, 496, 497, 498, 499, 504, 514, 524, 534, 540, 541, 542, 543, 544, 544, 545, 546, 547, 548, 549, 554, 564, 574, 584, 594
You can also numerically count your answers with computer code. Here is a script that will give you the answer (it's written in PHP, but it should translate to other languages).
$count = 0;
for ($i=400; $i<601; $i++) foreach (str_split($i) as $digit) if ($digit==4) $count++;
echo $count;
Again the answer is 140.
Wiki User
∙ 11y ago
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Wrote numbers 300 to 400 how many times did he write the digal number 3?
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If you write all of the counting numbers from 200 to 400,you will write the digit ' 5 ' forty times.
If you write down all the numbers from 300 to 400 how many times will you write the digit 3?
120 times.
Wrote numbers 300 to 400 how many times did he write the digal number 3?
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If you write 300 to 400 how many times do you write 3?
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How do you write 400 thousand in numbers?
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If you write down all the numbers between 300 to 400 how many times will you write the digit 3?
118 The following from rjsiekman; Think of it as the number of times the 3 will be written in the hundreds, tens, and ones column. This analysis assumes whole numbers; otherwise you can write a 3 an infinite number of times. In the hundreds, 301.....399 is 99 (because it is stated the numbers between 300 & 400; 300 is not included). In the tens, 3 will be written for 330....339 which adds another 10. In the ones, 3 will be written for 303, 313....393 which adds another 10. So, in total, the 3 will be written 119 times.
