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I thought of a three-digit number. If I add all the possible two-digit numbers
made by using only the digits of this number, then one third of this sum is
equal to the number I thought of. What is the number I thought of?

 May 17, 2020
 #1
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You thought of the number 432.

 May 17, 2020
 #2
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I believe that the number is 198.

 

Using these digits, two at a time (but there is no restriction that the same digit isn't used twice), the possibilities are:

11,18, 19, 81, 88, 89, 91, 98, 99

The sum is 594.

Dividing this by 3, gives us i98.

 May 17, 2020

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