Math CentralQuandaries & Queries


Question from Courtney, a student:

what is the largest 4-digit odd number you can make with 1 - 9. You can not repeat digits within a number

Hi Courtney,

Suppose the number is abcd. Think about place value

abcd = a × 1000 + b × 100 + c × 10 + d × 1

The digit that contributes the most to the number is a since a gets multiplied by 1000. Hence you want a to be as large as possible and thus a must be 9. The digit that contributes the next largest amount to the number is b since b gets multiplies by 100. The digit 9 has already been used so b must be 8.

Continue in this fashion. If the resulting number is even ask yourself "What is the least amount I can reduce this number and obtain an odd number?"


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