What Is A Heegner Number?

Logic Level 2

0 0 0 ÷ 0 \large \boxed{\phantom0} \: \boxed{\phantom0} \: \boxed{\phantom0} \div \boxed{\phantom0}

All the digits 6 , 7 , 8 6,7,8 and 9 9 are used exactly once to fill in the boxes above to form a ratio of a 3-digit integer and a 1-digit integer. If this ratio is an integer, what is the maximum possible value of this ratio?


The answer is 163.

View wiki
Pi Han Goh by Pi Han Goh , 30, Malaysia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Relevant wiki: Arithmetic Puzzles - Fill in the Blanks

For, the required integer to be maximum, the denominator must be minimum and numerator must be maximum.

So we start, with denominator as 6 6 and numerator whose first digit is 9 9 .

987 6 ≠ i n t e g e r \frac{987}{6} ≠ integer

986 6 ≠ i n t e g e r \frac{986}{6} ≠ integer

978 6 = i n t e g e r = 163 \frac{978}{6} = integer = \boxed{163}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

you wouldn't consider 986/6

Jeremy Ho - 5 years ago

Log in to reply

You can't repeat digits.

Abdur Rehman Zahid - 5 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...