In this number puzzle, 1+1+1+1 gives FOUR → R, 2+2+2+2 gives EIGHT → T, 3+3+3+3 gives TWELVE → E, 4+4+4+4 gives SIXTEEN → N. Then 5+5+5+5 corresponds to which final letter?

Introduction / Context:
This is a classic number and word pattern puzzle. At first glance, the expression "1 1 1 1 = R, 2 2 2 2 = T, 3 3 3 3 = E, 4 4 4 4 = N" looks mysterious, because it connects repeated digits with letters. The key to solving the puzzle is to realise that these repeated digits hint at addition and then at the English word for the resulting number. The letter on the right side comes from that word. The question then asks you to extend this pattern logically to "5 5 5 5" and decide which letter it should correspond to.

Given Data / Assumptions:

• We are given four examples: 1 1 1 1 → R, 2 2 2 2 → T, 3 3 3 3 → E, 4 4 4 4 → N.
• Each group of four identical digits is intended to be combined with addition, for example 1+1+1+1.
• The sum of the four identical digits is converted into an English number word (such as FOUR or EIGHT).
• The displayed capital letter (R, T, E, N) is taken from this English word in a consistent way.
• We must find the corresponding letter for the case 5 5 5 5 using the same hidden rule.

Concept / Approach:
The central idea is to translate the repeated digits into arithmetic, then into words, and finally into letters. First, treat "1 1 1 1" as 1+1+1+1, which equals 4. The number 4 is written as FOUR in English, and the given letter is R, the last letter of FOUR. Next, 2+2+2+2 equals 8. The number 8 is written as EIGHT, and the last letter of EIGHT is T, which matches the puzzle. Similarly, 3+3+3+3 is 12, written as TWELVE, whose last letter is E; and 4+4+4+4 is 16, written as SIXTEEN, whose last letter is N. In each case the letter on the right is the last letter of the English word for the sum.

Step-by-Step Solution:
Step 1: Convert the pattern "1 1 1 1" into an addition: 1+1+1+1 = 4 → FOUR → last letter R. This.matches the given mapping. Step 2: Convert "2 2 2 2" into 2+2+2+2 = 8 → EIGHT → last letter T. This also matches the given mapping. Step 3: Convert "3 3 3 3" into 3+3+3+3 = 12 → TWELVE → last letter E, which again matches the puzzle. Step 4: Convert "4 4 4 4" into 4+4+4+4 = 16 → SIXTEEN → last letter N, matching the final given letter. Step 5: Apply the same rule to "5 5 5 5". Compute 5+5+5+5 = 20. Step 6: Write 20 in English as TWENTY. The last letter of TWENTY is Y. Step 7: Therefore, according to exactly the same pattern, 5 5 5 5 must correspond to the letter Y.
Verification / Alternative check:
To verify the rule, you can recheck every given example and confirm that no other consistent interpretation works as cleanly. In all four base cases, the process of summing the four digits, converting to the English word, and then taking the final letter gives exactly the listed letters R, T, E, and N. Furthermore, there is no need to change the rule halfway through, since 5+5+5+5 is a natural continuation of the sequence. When we compute the sum as 20 and write TWENTY, the last letter is clearly Y, which fits neatly with the pattern seen before and does not contradict any of the given mappings.

Why Other Options Are Wrong:
Option Z does not correspond to any obvious feature of the word TWENTY. Option T might tempt some learners because T appears in TWENTY, but the rule is clearly about the last letter, not just any letter. Option X has no connection to any of the words FOUR, EIGHT, TWELVE, SIXTEEN, or TWENTY. Thus these alternatives do not follow the established pattern. Only Y arises naturally from the sustained logic of the puzzle and agrees with all earlier examples.

Common Pitfalls:
A common mistake is to look for patterns directly in the digits 1, 2, 3, and 4, or to treat the letters R, T, E, and N as initial letters of unknown words. Another pitfall is to focus on multiplication or concatenation (for example, 1111, 2222) instead of seeing that the repetition hints at repeated addition. When approaching such puzzles, it is useful to test small guesses like adding the digits and then thinking of number names. This strategy often reveals hidden word based patterns like the one in this question.

Final Answer:
Following the pattern, 5+5+5+5 = 20 → TWENTY, whose last letter is Y.