Using each of the 7 digits 1, 2, 3, 4, 5, 6, 7 only once, what is the difference between the smallest 4-digit number that can be made and the largest 3-digit number that can be made?
largest 4 digit number = 7654
smallest 3 digit number = 123
take the difference between them
smallest 4 digit > 1234
largest 3 digit > 765
1234 - 765
difference > 469
To find the smallest 4-digit number that can be made using the digits 1, 2, 3, 4, 5, 6, and 7 only once:
1. Start by arranging the digits in ascending order. The smallest digit is 1, so let's place it at the start: 1 _ _ _.
2. Next, find the smallest digit remaining, which is 2. Place it in the second position: 1 2 _ _.
3. Continue this process until all the digits are used: 1 2 3 4.
4. The smallest 4-digit number that can be formed is 1234.
To find the largest 3-digit number that can be made using the digits 1, 2, 3, 4, 5, 6, and 7 only once:
1. Start by arranging the digits in descending order. The largest digit is 7, so let's place it at the start: 7 _ _.
2. Next, find the largest digit remaining, which is 6. Place it in the second position: 7 6 _.
3. Continue this process until all the digits are used: 7 6 5.
4. The largest 3-digit number that can be formed is 765.
Now, calculate the difference between the smallest 4-digit number (1234) and the largest 3-digit number (765):
1234 - 765 = 469
Therefore, the difference between the smallest 4-digit number that can be made and the largest 3-digit number that can be made is 469.