## Monday, April 25, 2011

### In My Opinion, This is Hard to Do

This is a famous problem from 1882, to which a prize of \$1000 was awarded for the best solution. The task is to arrange the seven numbers 4, 5, 6, 7, 8, 9, and 0, and eight dots in such a way that an addition approximates the number 82 as close as possible. Each of the numbers can be used only once. The dots can be used in two ways: as decimal point and as symbol for a recurring decimal. For example, the fraction 1/3 can be written as
.
. 3

The dot on top of the three denotes that this number is repeated infinitely. If a group of numbers needs to be repeated, two dots are used: one to denote the beginning of the recurring part and one to denote the end of it. For example, the fraction 1/7 can be written as
.               .
. 1 4 2 8 5 7

Note that '0.5' is written as '.5'.

How close can you get to the number 82?

1. What, no takers?
.
80.5
..
.97
..
.46
_____
82

2. Well, that wasn't formatted very well. The first . is over the 5 in 80.5. The two dots under 80.5 should be directly over the 97. The two dots over .46 should be directly over the 46.

3. 80. (and then)

... .
97645

4. ^ Written around the same time, though took awhile to post due to dot formatting problems too. (Whatever the case, my answer was not entirely correct. Enjoy your day...)

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