Scale means base system..
Let number be ABC in base system 7.
(ABC)₇ = (CBA)₉
so a,b,c < 7 ..

49a+7b+c = 81c+9b+a
48a = 2b + 80c
24a-40c = b
8(3a-5c) = b
B can be multiple of 8 only so either 0,8.
since the base system is 7 so B = 8 is not possible.
Therefore only B = 0 is possible..

8(3a-5c) = 0
3a=5c
a : c = 5 : 3
so a = 5 , c = 3 same logic a,c <7

(503)₇ = 7²*5 + 7¹*0 + 7⁰*3
= 245 + 3 = 248 ✅

Unique (old) Number System™

Sunil Jhajhria

Ye scale kya h yha?

Scale means base system..
Let number be ABC in base system 7.
(ABC)₇ = (CBA)₉
so a,b,c < 7 ..

49a+7b+c = 81c+9b+a
48a = 2b + 80c
24a-40c = b
8(3a-5c) = b
B can be multiple of 8 only so either 0,8.
since the base system is 7 so B = 8 is not possible.
Therefore only B = 0 is possible..

8(3a-5c) = 0
3a=5c
a : c = 5 : 3
so a = 5 , c = 3 same logic a,c <7

(503)₇ = 7²*5 + 7¹*0 + 7⁰*3
= 245 + 3 = 248 ✅

hottg.com/number_system_ques/5274

679 viewsSaurabh Chaudhary ™, May 28, 2021 at 16:52