Calling Numbers Part 1

Logic Level 2

$\large 2 \square \div \square 5 = 2\div5$

What is the smallest number greater than 6 that can be placed in the $\square?$

Details and Assumptions :

Both boxes in the equation are equal in values.
This is an arithmetic puzzle. If you think that the number should be placed in the $\square$ is 789, then the equation $2789 \div 7895 = 2\div 5$ must be true. It does not represent the algebraic expression $2 \times \square \div \square \times 5$ .

The answer is 66.

1 solution

Vishnu Bhagyanath
Jul 16, 2015

If $x$ was a single digit number $\frac{20+x}{10x+5} = \frac 25 \Rightarrow x=6$ But since $x>6$ , we shall check the smallest 2 digit number. $\frac{200+x}{10x+5} = \frac 25 \Rightarrow x=66$ It is interesting to note that the series is $6,66,666,6666 ...$ for $n$ -digit $x$

Moderator note:

Can you prove your last line?

In reply to challenge master :

$\frac{20 \times 10^n + x}{10x+5}=\frac 25$

Where $n \in \mathbb{N}$

Cross multiplying and rearranging terms,

$x = \frac 23 (10^{n+1}-1)$

Vishnu Bhagyanath - 5 years, 11 months ago

An exactly similar approach....

Rishabh Tripathi - 5 years, 11 months ago

Calling Numbers Part 1

The answer is 66.

1 solution

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