Inspiration for Binary and 3

Write a program to accomplish following task.

Your friend Jack enters bits of a binary number (unit bit then two's bit then four's bit then ...). He will terminate by entering a non binary digit (i. e. anything other than 0 and 1). Each time he enters digit, tell him whether number formed so far is divisible by 3 (i.e. $11_2$ ) or not.

#ComputerScience

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Take the difference between sums of alternate digits. If it is 0 or is divisible by 3, then the number is divisible by 3. I'll let you think, why so?

Dhruv Somani - 4 years, 3 months ago

Analogus to "divisibility test for $11_{10}$ ", isn't it? Can you solve this one and post your solution.

Rushikesh Jogdand - 4 years, 3 months ago

The question to which you have linked. Is $B$ fixed? Then, $S$ contains $\le n$ nunbers or did you mean all such $2^n$ numbers?

Dhruv Somani - 4 years, 3 months ago

@Dhruv Somani – The file contains a single (large) binary number = B. The wording is meant to emitate input of digits (hence, unit digit come first, then two's...). The ideas is to put a digit to right of the number, check divisibility, do this till EOF.

Rushikesh Jogdand - 4 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$