On the 2005-2006 TMSCA regional number sense test, on number 77, it asks to determine to base of 113 if it equals 23 (base 10). How do I determine the base number now?

Very interesting problem. First thing is that it is probably a pretty low base I would be mentally trying 4 5 and 6 first. There is a way to do it but it becomes quadratic.

Oh yes, a fellow number sense maniac at my school found out that you could first subtract the ones place value from the base 10 number, then b^2+b would equal the remaining base 10 number. I have no idea how that works but it works!

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On the 2005-2006 TMSCA regional number sense test, on number 77, it asks to determine to base of 113 if it equals 23 (base 10). How do I determine the base number now?

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Very interesting problem. First thing is that it is probably a pretty low base I would be mentally trying 4 5 and 6 first. There is a way to do it but it becomes quadratic.

Oh yes, a fellow number sense maniac at my school found out that you could first subtract the ones place value from the base 10 number, then b^2+b would equal the remaining base 10 number. I have no idea how that works but it works!