Quandaries and Queries
 

 

I am a 3 digit number. My last digit is 3 times my first digit. My firat digit is twice my middle digit. What numbers am I? There are at least 2 correct answers? Thank you
 

 

One possible solution -
My last digit is 3 times my first digit:

This statement says alot. First, the last digit must be a multiple of 3, so it is either 3, 6 or 9. Second, given the last digit, we know the first digit must be 1, 2 or 3, respectiviely. Thus, the number is: 1_3, 2_6, or 3_9.

My first digit is twice my middle digit:

This statement says the first digit must be a multiple of 2, that is, the first digit is even. This means of the three possibilities generated above, only one can be used, namely, 2_6. Thus, the answer is 216.

Unless you allow 000 as a 3 digit number, there is only one possible answer!

Another solution -
Above I assumed the the units digit was the 3rd digit. In this solution, I will assume that units is 1st, tens is 2nd, and hundreds is 3rd.

My last digit is 3 times my first digit:

The possibilities now are: 3_1, 6_2, or 9_3. My first digit is twice my middle digit: First digit ie even so the only possibility from above is 6_2. Thus, the answer is 612. Again, a unique answer, although different from solution 1 since assumed a reversed order of digits.

Now I have a request for you: Please let me know if you find another solution, or discover if there is a problem with the wording of this question.

Paul
 
 

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