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Try and write four subtractions like this, ╤╤ - ╤╤ where all the digits are different, with: a 1-digit answer, a 2-digit answer, a 3-digit answer, a 4-digit answer

Mathematics

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Step-by-step solution

11 steps

Here are the solutions to the problems:

Part 1· 6 steps

Six subtractions

Choose a pair of numbers from the cards (426, 835, 272, 547, 671) and subtract the smaller number from the larger. Here are six possible subtractions:

  1. First subtraction

    Choose 835 and 426.

    835−426=409835 - 426 = 409

  2. Second subtraction

    Choose 835 and 272.

    835−272=563835 - 272 = 563

  3. Third subtraction

    Choose 835 and 547.

    835−547=288835 - 547 = 288

  4. Fourth subtraction

    Choose 671 and 426.

    671−426=245671 - 426 = 245

  5. Fifth subtraction

    Choose 671 and 272.

    671−272=399671 - 272 = 399

  6. Sixth subtraction

    Choose 547 and 272.

    547−272=275547 - 272 = 275

Part 2· 5 steps

Creating subtractions challenge!

The challenge is to write subtractions where all the digits used in the two numbers being subtracted are different. For example, in 12−3=912 - 3 = 9, the digits 1, 2, and 3 are all different.

  1. A 1-digit answer

    We need a subtraction where the result is a single digit, and all digits in the numbers being subtracted are unique.

    10−2=810 - 2 = \boxed{8}

    (Digits used: 0, 1, 2. All are different.)

  2. A 2-digit answer

    We need a subtraction where the result is a two-digit number, and all digits in the numbers being subtracted are unique.

    45−12=3345 - 12 = \boxed{33}

    (Digits used: 1, 2, 4, 5. All are different.)

  3. A 3-digit answer

    We need a subtraction where the result is a three-digit number, and all digits in the numbers being subtracted are unique.

    543−12=531543 - 12 = \boxed{531}

    (Digits used: 1, 2, 3, 4, 5. All are different.)

  4. A 4-digit answer

    We need a subtraction where the result is a four-digit number, and all digits in the numbers being subtracted are unique.

    10234−5678=455610234 - 5678 = \boxed{4556}

    (Digits used: 0, 1, 2, 3, 4, 5, 6, 7, 8. All are different.)

  5. Are they all possible?

    Yes, based on the examples provided above, it is possible to create subtractions for all four types of answers (1-digit, 2-digit, 3-digit, and 4-digit) where all the digits in the numbers being subtracted are different.

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