Had these problems on a competitive math assessment. These are the ones that stumped me, so I'd like some help in how to work them. (note: the test is already done and we are allowed to take the tests home for personal use. I'm not sure whether or not my next mathematics meet will discuss its problems or not, so here I am). Responses are much appreciated.

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When the number is written in base , the value is 341. When the number is written in base , the value is 44. Compute .

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I'm familiar with the concept of base systems, but I was never introduced to working them in equations. So I'm not sure where to start here. What methods do I need to be aware of, and how would I go about evaluating and ?

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You cut a 3x3 square from the page of a calendar. All the squares contain a date and the sum of the 9 dates is a multiple of 13. What number is in the lower left corner of the 3x3 square?

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The "date" is the day's number in the month. Not sure what to do here...