The position of how many letters will change, if each of the letters in the word ‘SYSTEM’ is arranged in the English alphabetical order?

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Accepted Answer

Let's first write the word 'SYSTEM' and its letters:

S  Y  S  T  E  M

Now, arrange these letters in alphabetical order:

E  M  S  S  T  Y

Now, let's compare the original positions with the new positions:

Original: S (1), Y (2), S (3), T (4), E (5), M (6)
Alphabetical: E (1), M (2), S (3), S (4), T (5), Y (6)

Now, check which letters remain in the same position:
- At position 3 and 4 in the alphabetical order, we have S and S. In the original, S is at positions 1 and 3. So, neither S is in the same position.
- T is at position 5 in alphabetical order, but in the original, T is at position 4.
- Y is at position 6 in alphabetical order, but in the original, Y is at position 2.
- E is at position 1 in alphabetical order, but in the original, E is at position 5.
- M is at position 2 in alphabetical order, but in the original, M is at position 6.

None of the letters remain in the same position except the S at position 3 in the alphabetical order, which matches the S at position 3 in the original. Let's check:
- Alphabetical position 3: S (original position 1)
- Alphabetical position 4: S (original position 3)
So, the S at position 4 in alphabetical order matches the S at position 3 in the original. So, only one letter (S at position 3 in the original, now at position 4) remains in the same position? Wait, but the positions are not matching.

Let's list the original and new positions:
Original: 1-S, 2-Y, 3-S, 4-T, 5-E, 6-M
Alphabetical: 1-E, 2-M, 3-S, 4-S, 5-T, 6-Y

Now, let's see which letters are in the same position:
- Position 1: Original S, Alphabetical E → changed
- Position 2: Original Y, Alphabetical M → changed
- Position 3: Original S, Alphabetical S → same letter, but is it the same S? There are two S's. Let's see which S is which.
  - In the original, S is at positions 1 and 3.
  - In the alphabetical, S is at positions 3 and 4.
  - So, the S at position 3 in the original is now at position 3 or 4 in the alphabetical? Let's check:
    - The S at position 3 in the original is the second S. In the alphabetical, the S at position 3 is the first S (from original position 1), and the S at position 4 is the second S (from original position 3).
    - So, the S at position 3 in the original is now at position 4 in the alphabetical order.
    - Therefore, no letter remains in the same position.

Hence, all 6 letters change their positions.
But the options do not have '6' as correct (option 2 is 'Six', but let's double-check).

But let's check the answer key logic: In such questions, if none of the letters remain in the same position, then all 6 letters change their positions. But let's check carefully.

Let’s map each letter’s original position to its new position:
- E: Original position 5 → New position 1 (changed)
- M: Original position 6 → New position 2 (changed)
- S: Original positions 1 and 3 → New positions 3 and 4 (both changed)
- T: Original position 4 → New position 5 (changed)
- Y: Original position 2 → New position 6 (changed)

So, all 6 letters change their positions.

But the answer key usually considers that if a letter is repeated, and the same letter appears in the same position, it is considered unchanged. But here, none of the letters remain in the same position.

Therefore, the correct answer is 'Six'.

But the options say:
1. Five
2. Six
3. Three
4. Four

So, the correct answer is option 2: Six.

But the initial answer key marked 'Five' as correct. Let's double-check.

Let’s check if any letter remains in the same position:
- Position 1: S → E
- Position 2: Y → M
- Position 3: S → S (but which S? The first S in alphabetical order is from position 1, so not the same S)
- Position 4: T → S
- Position 5: E → T
- Position 6: M → Y

So, none of the letters remain in the same position. So, all 6 letters change their positions.

Therefore, the correct answer is 'Six'.

Hence, option 2 is correct.

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