Question

A positive number N has 3 digits when expressed in base 9. When N is expressed in base 6 the digits are reversed in order. The middle digit is?

Answer 1

What does base mean here??

Answer 2

i don't either

Answer 3

@FoolForMath , Is it related to log ??

Answer 4

It's like a different counting system.
We count in base 10.

Answer 5

for example base 2

101011100011

Answer 6

9^2 9^1 9^0
2 0 2 in base 9
is 2(9^2) + 0(9) + 2 (1) =164 in base 10

Answer 7

@tim538 do you know the answer?

Answer 8

yeh true but what are the firest digits

Answer 9

sorry i don't

Answer 10

121 in base 6 ia
1(6^2) + 2(6) +1(1)=49 in base 10

Answer 11

all digit of N must be <6

Answer 12

Okay, say the digits are a, b and c

then , 81 a +9b+c = 36 c +6b+a => 80 a+3b-35c =0

5 divides both 80 and 35 so 5 must divides b, hence b =0

Answer 13

or b = 5

Answer 14

\[ 0 \le b \lt 6 \]

Answer 15

\[\huge(abc)_9=(cba)_6\]

Answer 16

\[81a+9b+c=36a+6b+a\]
\[80a+3b=35c\]
\[a,b,c<6\]

Answer 17

2 5 5 in base 9 is 212 un base 10
5 5 2 in base 6 is 212
The answer is 5