Math CentralQuandaries & Queries


Denise, a student:

a number has 4 different odd digits. the difference between the greatest digit and the least digit is 6, the number is greater than 2,000 and less than 3,160. what is the number?

Hi Denise,

Since all 4 digits must be odd, then the number cannot be in the range of 2000 - 2999. So we know that the number must begin with a 3. Since 0 is not an odd number the so the digits cannot be 0. So we know than the number is truly between 3111 - 3159. The odd digits are 1, 3, 5, 7, 9, which ones have a difference of 6 that have not been used?

Hope this helps,


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