2
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Rules: Make the numbers 1-100 using eight 8s. Use the operations +, -, *, /, exponentiation and !.

No rounding, e.g. you may not get $9$ by doing $\sqrt{88} = 9.38... \approx 9$. No using other digits

Multi digit numbers (concatenation) and the decimal $.8$ is allowed.

Use overhead lines i.e. \bar{} or \overline{} for recurring decimals: e.g. $.\bar{8}= .88... = \frac{8}{9}$.

Multifactorial is allowed but each multifactorial can’t have more than $10$ factorials, e.g. $(8+8)!!!!!!!!!!=16*6=96$ is the maximum.

Subfactorials are allowed, i.e. $!n=\lfloor{\frac{n!}{e}+\frac{1}{2}}\rfloor$.

Have Fun!

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8
  • 2
    $\begingroup$ I see that this puzzle is downvoted without comment, but a very similar one was acceptable and popular. Please leave comments when possible on how a post might be improved. $\endgroup$
    – Galen
    Apr 24, 2020 at 0:44
  • 1
    $\begingroup$ Your six 6's. Overall, people liked it. $\endgroup$
    – Galen
    Apr 24, 2020 at 0:47
  • 9
    $\begingroup$ To be fair, sometimes the puzzles are similar yet the responses may be different: people may be bored or uninterested to see roughly identical puzzles especially in a short time. In this case, it's just changing from 6 to 8. Plus, asking 100 equations is a lot and tedious too for other people. This is my opinion anyway. $\endgroup$
    – athin
    Apr 24, 2020 at 1:55
  • 2
    $\begingroup$ @athin I disagree.It's not Matheinstein's fault if another similar puzzle was posted and you shouldn't downvoted only for this reason (upvoting for support). As for the 100 equations what about a community wiki answer? $\endgroup$
    – melfnt
    Apr 24, 2020 at 6:01
  • 4
    $\begingroup$ @melfnt Well, I'm not downvoting this in the first place tbh... Anyway another similar puzzle of six 6s is also written by the same person... And yeah community wiki answer should be ok, but still doesn't mean this has to gain upvotes. People upvote whenever they see a puzzle interesting, thoughtful, nice in several ways, a high-effort, etc. People downvote if it's opposite. Most people don't vote if they see this as a neutral puzzle (me in this one). $\endgroup$
    – athin
    Apr 24, 2020 at 7:38

1 Answer 1

7
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All 100 complete!

(Using $8! = 40320,\ 8!!=384,\ 8!!! = 80$)

$1 = 8+8+8+8/8-8-8-8$
$2 = 8+8+8/8+8/8-8-8$
$3 = 8+8/8+8/8+8/8-8$
$4 = 8+8+8 \times 8 \times .8+.8-8 \times 8$
$5 = 8+8/.\overline{8}+8 \times .8 \times .\overline{8}-.8-8$
$6 = 8+8-8-8/8-.\overline{8}-.\overline{8}/8$
$7 = 8+8+8-8-8-.\overline{8}-.\overline{8}/8$
$8 = 8+8+8-8 \times .8-.8-.8-8$
$9 = 8+8+8+8/.\overline{8}+.\overline{8}-8-8$
$10 = 8+8+8/8+8/.\overline{8}+.\overline{8}-8$
$11 = 8+8+.8-8/.\overline{8}-.8 \times .\overline{8} \times 8$
$12 = 8+8+8 \times .8 \times .\overline{8}-.8-.\overline{8}-8$
$13 = 8+8-8/8-8/8-8/8$
$14 = 8+8+8-8-8/8-8/8$
$15 = 8+8+8+8-8-8-8/8$
$16 = 8+8+8+8+8-8-8-8$
$17 = 8+8+8+8+8/8-8-8$
$18 = 8+8+8+8/8+8/8-8$
$19 = 8+8+8/8+8/8+8/8$
$20 = 8+8+8+.8+.8+.8-.8 \times 8$
$21 = 8!!/8/8+8+8-.\overline{8}-.\overline{8}/8$
$22 = 8!!/8/8+8+.8+.8+.8 \times 8$
$23 = 8!!/8-8-8-8-.\overline{8}-.\overline{8}/8$
$24 = 8!!/8-8-8-.8-.8-.8 \times 8$
$25 = 8!!/8+8/.\overline{8}+.\overline{8}-8-8-8$
$26 = 8!!!/8+8+8+8+8-8-8$
$27 = 8!!/.8+8+8+8-.8-8/8$
$28 = 8!!/8+.8-8-8 \times .8-.8 \times 8$
$29 = 8!!/8/8+8+8+8-8/8$
$30 = 8!!/8-8-8-8/8-8/8$
$31 = 8!!/8+8-8-8-8-8/8$
$32 = 8!!/8+8+8-8-8-8-8$
$33 = 8!!/8+8+8/8-8-8-8$
$34 = 8!!/8+8/8+8/8-8-8$
$35 = 8!!!/8+8+8+8+.\overline{8}+.\overline{8}/8$
$36 = 8!!/8+8 \times 8 \times .8+.8-8 \times 8$
$37 = 8!!!/.8+8 \times 8 \times .8+.8-8-8$
$38 = 8!!/8-8-8/8-.\overline{8}-.\overline{8}/8$
$39 = 8!!/8+8-8-8-.\overline{8}-.\overline{8}/8$
$40 = 8!!/8+8/8-8-.\overline{8}-.\overline{8}/8$
$41 = 8!!/8+8+8/.\overline{8}+.\overline{8}-8-8$
$42 = 8!!/8+8/8+8/.\overline{8}+.\overline{8}-8$
$43 = 8!!/8/.8-8-.8+8 \times .8 \times 8$
$44 = 8!!/8+8+.8-8 \times .8-.8 \times 8$
$45 = 8!!/8-8/8-8/8-8/8$
$46 = 8!!/8+8-8-8/8-8/8$
$47 = 8!!/8+8+8-8-8-8/8$
$48 = 8!!/8+8+8+8-8-8-8$
$49 = 8!!/8+8+8+8/8-8-8$
$50 = 8!!/8+8+8/8+8/8-8$
$51 = 8!!/8+8/8+8/8+8/8$
$52 = 8!!/8+8 \times .8+8 \times .8-.8-8$
$53 = 8!!!/8/8 \times .8+.8+8 \times .8 \times 8$
$54 = 8!!/8+8-8/8-.\overline{8}-.\overline{8}/8$
$55 = 8!!/8+8+8-8-.\overline{8}-.\overline{8}/8$
$56 = 8!!/8+8+8/8-.\overline{8}-.\overline{8}/8$
$57 = 8!!/8+8+8+8/.\overline{8}+.\overline{8}-8$
$58 = 8!!/8+8+8/8+.\overline{8}+.\overline{8}/8$
$59 = 8!!/8/.8+8-.8+8 \times .8 \times 8$
$60 = 8!!/8+8 \times 8-.8-8 \times .8 \times 8$
$61 = 8!!!-8/.\overline{8}+8+.8+8 \times .8 \times 8$
$62 = 8!!!-8-8-8/8-.\overline{8}-.\overline{8}/8$
$63 = 8!!!-8+8-8-8-.\overline{8}-.\overline{8}/8$
$64 = 8!!!-8+8-8-.8-.8-.8 \times 8$
$65 = 8!!!-8+8+8/.\overline{8}+.\overline{8}-8-8$
$66 = 8!!!-8+8/8+8/.\overline{8}+.\overline{8}-8$
$67 = 8!!!-8+.8-8/.\overline{8}-.8 \times .\overline{8} \times 8$
$68 = 8!!!-8+8 \times .8 \times .\overline{8}-.8-.\overline{8}-8$
$69 = 8!!!-8-8/8-8/8-8/8$
$70 = 8!!!-8+8-8-8/8-8/8$
$71 = 8!!!-8+8+8-8-8-8/8$
$72 = 8!!!-8+8+8+8-8-8-8$
$73 = 8!!!-8+8+8+8/8-8-8$
$74 = 8!!!-8+8+8/8+8/8-8$
$75 = 8!!!-8+8/8+8/8+8/8$
$76 = 8!!!-8+8+.8+.\overline{8}-.8 \times .\overline{8} \times 8$
$77 = 8!!!-8+8/.\overline{8}-.8+.8 \times .\overline{8} \times 8$
$78 = 8!!!-8+8-8/8-.\overline{8}-.\overline{8}/8$
$79 = 8!!!-8+8+8-8-.\overline{8}-.\overline{8}/8$
$80 = 8!!!-8+8+8-.8-.8-.8 \times 8$
$81 = 8!!!+8+8+8/.\overline{8}+.\overline{8}-8-8$
$82 = 8!!!+8+8/8+8/.\overline{8}+.\overline{8}-8$
$83 = 8!!!+8+.8-8/.\overline{8}-.8 \times .\overline{8} \times 8$
$84 = 8!!!+8+8 \times .8 \times .\overline{8}-.8-.\overline{8}-8$
$85 = 8!!!+8-8/8-8/8-8/8$
$86 = 8!!!+8+8-8-8/8-8/8$
$87 = 8!!!+8+8+8-8-8-8/8$
$88 = 8!!!+8+8+8+8-8-8-8$
$89 = 8!!!+8+8+8+8/8-8-8$
$90 = 8!!!+8+8+8/8+8/8-8$
$91 = 8!!!+8+8/8+8/8+8/8$
$92 = 8!!!+8+8+.8+.\overline{8}-.8 \times .\overline{8} \times 8$
$93 = 8!!!+8+8/.\overline{8}-.8+.8 \times .\overline{8} \times 8$
$94 = 8!!!+8+8-8/8-.\overline{8}-.\overline{8}/8$
$95 = 8!!!+8+8+8-8-.\overline{8}-.\overline{8}/8$
$96 = 8!!!+8+8+8-.8-.8-.8 \times 8$
$97 = 8!!!+8+8+8+8/.\overline{8}+.\overline{8}-8$
$98 = 8!!!+8+8+8/8+.\overline{8}+.\overline{8}/8$
$99 = 8!!!+8/8+8+8+8+8 \times 8$
$100 = 8!!!+8+8-.8-.\overline{8}+.8 \times .\overline{8} \times 8$

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