Counting the Number of Times Digit 4 Appears from 1 to 1234

In this detailed analysis, we aim to determine how many times the digit '4' appears when a computer prints all numbers from 1 to 1234. To achieve this, we will break the numbers down into their respective place values—thousands, hundreds, tens, and units.

Analysis by Digit Place

Units Place

Numbers with '4' in the units place can be listed as follows: 4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 104, 114, 124, 134, 144, 154, 164, 174, 184, 194, 204, 214, 224, 234, 244, 254, 264, 274, 284, 294, 304, 314, 324, 334, 344, 354, 364, 374, 384, 394, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 504, 514, 524, 534, 544, 554, 564, 574, 584, 594, 604, 614, 624, 634, 644, 654, 664, 674, 684, 694, 704, 714, 724, 734, 744, 754, 764, 774, 784, 794, 804, 814, 824, 834, 844, 854, 864, 874, 884, 894, 904, 914, 924, 934, 944, 954, 964, 974, 984, 994, 1004, 1014, 1024, 1034, 1044, 1054, 1064, 1074, 1084, 1094, 1104, 1114, 1124, 1134, 1144, 1154, 1164, 1174, 1184, 1194, 1204, 1214, 1224, 1234.

Counting these occurrences, we find there are 124 instances of the digit '4' in the units place.

Tens Place

Numbers with '4' in the tens place are: 40-49, 140-149, 240-249, 340-349, 440-449, 540-549, 640-649, 740-749, 840-849, 940-949, 1040-1049, 1140-1149, 1240-1249.

Each range contains 10 occurrences of the digit '4'. There are 12 such ranges, making a total of 120 instances of '4' in the tens place.

Hundreds Place

Numbers with '4' in the hundreds place range from 400 to 499, which includes 100 occurrences of the digit '4'.

Thousands Place

The digit '4' does not appear in the thousands place for numbers from 1 to 1234.

Total Count

Summing up all the occurrences, we get the following:

Total occurrences of 4: 344

Thus, the digit '4' appears 344 times when printing all the numbers from 1 to 1234.