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!

## 3 comments

## Jonathan Ye

February 11, 2018 at 2:32 am (UTC 0) Link to this comment

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?

## anthony gillespey

February 15, 2018 at 8:02 pm (UTC 0) Link to this comment

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.

## Jonathan Ye

February 19, 2018 at 5:40 am (UTC 0) Link to this comment

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!