+0

# base

0
132
4

The following addition problem is not correct if the numbers are interpreted as base 10 numbers. in what number base is the problem correct?

66+87+85+48

Aug 22, 2022

#1
0

that's not a problem...

Aug 22, 2022
#2
0

sorry.

The following addition problem is not correct if the numbers are interpreted as base 10 numbers. in what number base is the problem correct?

66+87+85+48=132

Aug 22, 2022
#3
0

Let the base be b. Off the bat, we know that $$b>8$$.

If we added everything, it would look something like this:

66

87

+      85

48

$$\overline{\color{white}{wwwwww}}$$

132

Adding up the ones digit gives us 26, so we have $$26 \mod b = 2$$

The only options for b are b = 12 or 24.

If b = 12, the sum of the ones digit would be $$22_{12}$$, so we could carry the 2 to the tens column. Adding everything up would give us $${24}_{12}$$, so our answer would be $$242_{12}$$.

This means that the base is $$\color{brown}\boxed{24}$$.

(Add it up to see for yourself.)

Aug 23, 2022
#4
+1

You could also look at it like this: Aug 23, 2022