Admin: Add Problem 42 page with problem statement, solution approach, and code link (via create-page on MediaWiki MCP Server)

2026-06-16T14:12:31Z

Add Problem 42 page with problem statement, solution approach, and code link (via create-page on MediaWiki MCP Server)

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==Problem Statement==

The nth term of the sequence of triangle numbers is given by:

<math>
t_n = \frac{1}{2} n (n + 1)
</math>

The first ten triangle numbers are:

<math>
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, \dots
</math>

By converting each letter in a word to a number corresponding to its alphabetical position (A=1, B=2, ..., Z=26) and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t_{10}. If the word value is a triangle number, then the word is called a triangle word.

Using words.txt, a 16K text file containing nearly two-thousand common English words, find the number of triangle words.

==Approach==

===Pre-compute Triangle Numbers===

Generate all triangle numbers up to a sufficient bound. The longest word in the file yields a word value well under 5,000, so pre-computing triangle numbers for n = 1 to 100 (giving t_{100} = 5050) is more than adequate. Store these in a HashSet for O(1) lookup.

===Parse the Word File===

The file words.txt contains comma-separated, double-quoted words (e.g., "A","ABILITY","ABLE",...). Split on commas, strip the surrounding quotes, and trim whitespace.

===Compute Word Values===

For each word:
* Convert to uppercase
* Iterate over each character, computing its value as (c - 'A' + 1)
* Sum all character values to obtain the word value

===Check Against Triangle Numbers===

If the word value is contained in the pre-computed set of triangle numbers, increment the count.

===Return the Count===

After processing all words, return the total count of triangle words.

==Solution==

Link: https://git.charlesreid1.com/cs/euler/src/branch/main/java/Problem042.java

==Flags==

{{ProjectEulerFlag}}

Project Euler/42 - Revision history

Admin: Add Problem 42 page with problem statement, solution approach, and code link (via create-page on MediaWiki MCP Server)