Mathematics
Write the greatest and the smallest four-digit numbers using four different digits with the conditions:
(i) Digit 3 always at hundred's place.
(ii) Digit 0 always at ten's place.
Answer
(i) Digit 3 always at hundred's place.
The number is of the form _ 3 _ _ (with all four digits different).
For the greatest 4-digit number, fill the remaining places with the largest distinct digits other than 3. Use 9 at thousands, 8 at tens and 7 at units.
Greatest 4-digit number = 9387.
For the smallest 4-digit number, the thousand's place cannot be 0. Place 1 (smallest non-zero, ≠ 3) at thousands, 3 at hundreds, 0 at tens and 2 at units.
Smallest 4-digit number = 1302.
Hence, the greatest 4-digit number is 9,387 and the smallest 4-digit number is 1,302.
(ii) Digit 0 always at ten's place.
The number is of the form _ _ 0 _ (with all four digits different).
For the greatest 4-digit number, fill the remaining places with the largest distinct digits other than 0. Use 9 at thousands, 8 at hundreds and 7 at units.
Greatest 4-digit number = 9807.
For the smallest 4-digit number, the thousand's place cannot be 0. Place 1 (smallest non-zero) at thousands, 2 at hundreds, 0 at tens and 3 at units.
Smallest 4-digit number = 1203.
Hence, the greatest 4-digit number is 9,807 and the smallest 4-digit number is 1,203.
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