-3
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With the given numbers I need to make:

$7 \circ 8 \circ 7 \circ 7 \circ 8 \circ 3 = 100$

Using only the following operators:

$+\space-\space\times\space\div$

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7
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$7 \times 8 + 7 \times 7 - 8 + 3 = 100$

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  • $\begingroup$ This is pretty much it if we can't use parenthesis.. +1 $\endgroup$ – Raystafarian Nov 30 '15 at 16:30
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General "Countdown" arithmetic puzzle solution !!

Some Unix Shells have a property called 'brace expansion'

The usage varies between csh and bash but is something like this:

echo {a,i}{s,t}

Outputs:

as at is it

This can be used to solve the "Countdown" letters puzzle, simply have 9 consecutive braces with all 9 letters in each. If you don't know Countdown, you can use this to find Scrabble™ words, if you add a final brace at the end like {'\n'} you even get one result per line so you can pipe output through sort or usr/dict

So how do we do the Arithmetic puzzle ?

If we are given the integers 2,4,5

Alternate braces containing integers and operators:

set array {2,4,5}{+,-,\*,/}{2,4,5}…{'\n'} # * escaped to avoid wildcard

This gives:

2+2-4…
2-3*4…

Every permutation of integer and operator. Finally,

foreach s in (array) {echo $s ; eval $s} | sort

Evaluates all the expressions and even sorts them so you can find the integer you are looking for and the expression which created it.

"Countdown"™ Solved !!!

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