Grade 5

Encourage partial solutions, letting students build on each other’s work. Also, encourage students to question their results by asking “could there be more than one such number?”

Grace thought of a certain number in the billions. Each digit in this number is used only once. The number is odd, and there is only one odd number in the billions greater than it (without re-using any digits). What must this number be?

- A number in the billions has 10 digits. There are exactly 10 different digits so Grace’s number must use them all, exactly once. It can’t start with 0; it can’t end with an even digit.
- The greatest possible such number is 9,876,543,201.
- The next greatest number is 9,876, 543, 021, so that’s Grace’s number.

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