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Using the following rules only, Express the numbers from 50 to 100 using only digits in the number. Concise with minimum number of characters is preferred.

No concatenation of numbers allowed.

Only, plus, minus, division, multiplication(use dot), exponentiation, factorial, brackets where needed are allowed.

No multiple factorials and exponents allowed.

Vinculum(compliments of 10) allowed if you prefer. For example, 3 underlined is 7...9 underlined is 1.

See examples..in the picture..in red...blue ..normal way

I have filled in some..not necessarily optimum.

enter image description here

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  • $\begingroup$ So what's the question, exactly? Do you have to optimize every single one of these, or just accomplish them? $\endgroup$ – Deusovi Jun 18 at 17:33
  • $\begingroup$ Concise form is preferred..otherwise one can write long expressions for any number $\endgroup$ – Uvc Jun 18 at 17:35
  • $\begingroup$ Only for 1 to 9..if you see what I have written for 77...you can see it’s useful..very useful in simplifying various math operations. $\endgroup$ – Uvc Jun 18 at 17:37
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    $\begingroup$ The concise form is "preferred", but what counts as a solution? This seems like an activity, not a puzzle. $\endgroup$ – Deusovi Jun 18 at 17:44
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    $\begingroup$ So, are you required to find the optimal path for every number? What counts as a solution? The question doesn't ask for the optimal path, meaning there's not really much puzzle here. It sounds like you're treating this as primarily an activity for people to participate in, rather than a puzzle for people to solve. $\endgroup$ – Deusovi Jun 18 at 18:02
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Using the Vinculum:

$\underline{a}=10-a$

we have:

$\overline{ab}=10a+b=a(a+\underline{a})+b$, which solves all of them.

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  • $\begingroup$ That is not what it is intended for..it is trivial solution..you are technically correct $\endgroup$ – Uvc Jun 18 at 17:52

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