Four-digit numbers are to be formed using the digits 1, 2, 3 and 4; and none of these four digits are repeated in any manner. Further, 1. 2 and 3 are not to immediately follow each other 2. 1 is not to be immediately followed by 3 3. 4 is not to appear at the last place 4. 1 is not to appear at the first place How many different numbers can be formed ?

• Since 1 cannot be at the first place, the first digit must be 2, 3, or 4.

• If the first digit is 2, the second cannot be 3 (Rule 1), so it must be 1 or 4. If 2-1, the next cannot be 3 (Rule 2), so it must be 4, leaving 3 for the last: 2143. If 2-4, the next can be 1 or 3. If 2-4-1, last is 3: 2413. If 2-4-3, last is 1: 2431. Total 3 numbers.

• If the first digit is 3, the second cannot be 2 (Rule 1), so it must be 1 or 4. If 3-1, the next cannot be 3 (already used) but Rule 2 says 1 not followed by 3 (irrelevant here as 3 is used), so next is 2 or 4. If 3-1-2, last is 4: 3124. If 3-1-4, last is 2: 3142. If 3-4, next is 1 or 2. If 3-4-1, last is 2: 3412. If 3-4-2, last is 1: 3421. Total 4 numbers.

• If the first digit is 4, the second can be 1, 2, or 3. If 4-1, next cannot be 3 (Rule 2), so next is 2, last is 3: 4123. If 4-2, next cannot be 3 (Rule 1), so next is 1, last is 3: 4213. If 4-3, next is 1 or 2. If 4-3-1, last is 2: 4312. If 4-3-2, last is 1: 4321. Total 4 numbers.

• Wait, let's re-evaluate Rule 3: 4 is not to appear at the last place. In the 'First digit 2' case: 2143 (ends in 3, ok), 2413 (ends in 3, ok), 2431 (ends in 1, ok). In 'First digit 3' case: 3124 (ends in 4, INVALID), 3142 (ends in 2, ok), 3412 (ends in 2, ok), 3421 (ends in 1, ok). So 3124 is removed. In 'First digit 4' case: 4123 (ends in 3, ok), 4213 (ends in 3, ok), 4312 (ends in 2, ok), 4321 (ends in 1, ok).

• Valid numbers: 2143, 2413, 2431, 3142, 3412, 3421, 4123, 4213, 4312, 4321. That is 10 numbers? Let me re-check Rule 1: 2 and 3 not immediately follow each other. 2431 has 3-1, ok. 4312 has 3-1, ok. 4321 has 3-2, INVALID. So 4321 is removed.

• Let's list carefully:

1. Starts with 2: 2143 (ok), 2413 (ok), 2431 (ok). (3 numbers)

2. Starts with 3: 3124 (ends 4, invalid), 3142 (ok), 3412 (ok), 3421 (ok). (3 numbers)

3. Starts with 4: 4123 (ok), 4213 (ok), 4312 (ok), 4321 (3-2 adjacent, invalid). (3 numbers)

• Total valid numbers: 3 + 3 + 3 = 9? No, wait. 2431: 2-4-3-1. 2 and 3 are not adjacent. 1 is not followed by 3. 4 is not last. 1 is not first. Valid.

• Let's re-check 3421: 3-4-2-1. 2 and 3 not adjacent. 1 not followed by 3. 4 not last. 1 not first. Valid.

• Let's re-check 4312: 4-3-1-2. 2 and 3 not adjacent. 1 not followed by 3. 4 not last. 1 not first. Valid.

• Let's re-check 4123: 4-1-2-3. 2 and 3 adjacent? No, 2-3 is at the end. Rule 1 says 2 and 3 are not to immediately follow each other. So 4123 is INVALID.

• Let's re-check 4213: 4-2-1-3. 2 and 3 not adjacent. 1 followed by 3? Yes, 1-3 is at the end. Rule 2 says 1 is not to be immediately followed by 3. So 4213 is INVALID.

• Let's re-check 2143: 2-1-4-3. 2-3 not adjacent. 1-4 not 1-3. 4 not last. 1 not first. Valid.

• Let's re-check 2413: 2-4-1-3. 2-3 not adjacent. 1-3 adjacent. Rule 2 violation. INVALID.

• Let's re-check 2431: 2-4-3-1. 2-3 not adjacent. 3-1 not 1-3. 4 not last. 1 not first. Valid.

• Let's re-check 3142: 3-1-4-2. 3-1 not 2-3. 1-4 not 1-3. 4 not last. 1 not first. Valid.

• Let's re-check 3412: 3-4-1-2. 3-4 not 2-3. 1-2 not 1-3. 4 not last. 1 not first. Valid.

• Let's re-check 3421: 3-4-2-1. 3-4 not 2-3. 2-1 not 1-3. 4 not last. 1 not first. Valid.

• Let's re-check 4312: 4-3-1-2. 4-3 not 2-3. 3-1 not 1-3. 4 not last. 1 not first. Valid.

• Valid numbers: 2143, 2431, 3142, 3412, 3421, 4312. Total 6.

• Therefore, the answer is 6.