Brain Out Level 127

Overview

This is a counting question rather than an object puzzle: you must write every whole number from 1 through 199 and tally how many times the digit 1 appears in all those writings. The trap is to count numbers that contain a 1 instead of counting every occurrence of the digit, including repeated 1s within the same number. The correct total entered in the field is 140.
The prompt asks about writing out every integer, which means repeated digits inside one number must each be counted, not just the numbers that contain a 1.

• Difficulty: Regular
• Estimated moves: 2

Step-by-Step Solution

1. Break the problem by digit place instead of listing numbers one by one. Count the occurrences of 1 in the hundreds, tens, and units positions separately.
2. For the hundreds place, every number from 100 to 199 begins with a 1, giving 100 hundreds-digit occurrences of the digit.
3. For the tens place, 1 appears in the tens position for 10 to 19, 110 to 119, and the other full tens groups across 1 to 199; tally these groups to add the tens occurrences.
4. For the units place, 1 appears every ten numbers, such as 1, 11, 21 and onward, up to 191; tally those recurring unit digits.
5. Add the three place totals together and enter 140 in the answer field, then confirm. The green check appears when the digit count matches.

Split the tally by place value to keep the count organized: list the hundreds positions, then tens, then units, and write down how many times a 1 appears in each group. Add the three place totals together rather than scanning the numbers loosely, because loose scanning misses repeated 1s in numbers like 111 and 119. Once the combined total reaches 140, enter it in the field and confirm. The green check appears when the digit count matches, so double-check the units cycle before submitting.

Strategy & Reasoning

A digit tally counts positions, not numbers. A number like 111 contributes three separate 1s, so grouping by place value avoids double counting and missed repeats. Splitting hundreds, tens, and units makes the arithmetic repeatable: each place cycles through its own pattern across the range, and the sum of those cycles gives the total 140 that the level expects. Digit-counting puzzles reward place-by-place arithmetic over eyeballing the list. Grouping by hundreds, tens, and units makes each cycle repeatable and exposes repeated digits in the same number, and the final 140 is the sum of those separate cycles rather than a count of how many numbers happen to contain a 1.

Tips & Common Mistakes

• Count the digit itself each time it appears; a number like 111 counts as three ones, not one.
• Separate the hundreds, tens, and units positions so you do not forget repeats inside a number.
• Do not answer with the number of numbers that contain a 1; the question asks for occurrences of the digit.