The Faded Document Puzzle

I had posted this as a problem earlier, but I think some people were easily using option analysis to solve it, so I am putting it as a note.

The task is to fill in the blanks with the right digits. Only an 8 is visible. There may be other 8s in the document.

It looks difficult, but is pretty simple. You just have to imagine you are doing long division and see what constraints arise from that.

The source is Joseph Degrazia, Math Tricks, Twisters and Riddles.

Easy Math Editor

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
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`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

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

Firstly, there should be a zero before and after the 8 in the quotient-only then is the division possible, following the rules of 'carry-down'. Next, looking at the second line of division-a 2-digit divisor multiplied by 8 gives a 2-digit number. This is only true if the divisor is 10, 11 or 12. Next, looking at the first line of division, a 2-digit divisor multiplied by a one-digit number gives a 3-digit number. This can only happen if the divisor is 12 and the first digit of the quotient is 9.12*9=108 Apply the same logic in the last line of the division. Then fill in the few remaining blanks-it becomes self-evident how to.

Sachetan Debray - 5 months, 2 weeks 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}`	$\boxed{123}$