# Make the numbers 1-100 using six 6s

Rules:
Make the numbers 1-100 using six 6s
Use the operations + - * / exponentiation and !
No Rounding as in $$((6 - (6 + 6) / 6) + 6!!) / 6 = 9$$
No using other digits
Multi digit numbers and .6 is allowed
Use overhead lines for recurring decimals: $$.\overline{6} = .66... = \frac{2}{3}$$
Multifactorial is allowed but each multifactorial can’t have more than 10 factorials: $$(6+6)!!!!!!!=12*5=60$$
Subfactorials are allowed: $$!n=\lfloor{\frac{n!}{e}+\frac{1}{2}}\rfloor$$
Have Fun!

• Um, isn't 1-100 kinda too much to ask for in one puzzle? 😅 Commented Apr 23, 2020 at 8:59
• Why was this closed? It is clearly focused on 1 problem. Commented Apr 23, 2020 at 11:45
• @JMP It's only punishment if you don't like math. I found this fun and I was able to complete it in a reasonable amount of time (less than 2 hours). Commented Apr 23, 2020 at 11:51
• Yeah why is it closed? There are other puzzles out there that are also 1-100 but they are still open! Commented Apr 23, 2020 at 11:52
• Agreed, and voted to reopen. Commented Apr 23, 2020 at 12:04

### All 100 complete!

(Using $$6! = 720,\ 6!! = 48$$)

$$6+6+6/6-6-6 = 1$$

$$6+6/6+6/6-6 = 2$$

$$6+6+.6-6-.6 \times 6 = 3$$

$$6+6+6 \times .\overline{6}-6-6 = 4$$

$$6+6-.6-.6 \times .\overline{6}-6 = 5$$

$$6+.6+.6 \times .\overline{6}-6/6 = 6$$

$$6+6+.6+.6 \times .\overline{6}-6 = 7$$

$$6+6+6-6-.\overline{6} \times 6 = 8$$

$$6+6+6/6-.\overline{6} \times 6 = 9$$

$$6+6+.\overline{6}-.\overline{6} \times .\overline{6} \times 6 = 10$$

$$6+6+6-6-6/6 = 11$$

$$6+6+6+6-6-6 = 12$$

$$6+6+6+6/6-6 = 13$$

$$6+6+6/6+6/6 = 14$$

$$6+6+6 \times .\overline{6}-6/6 = 15$$

$$6+6+6+6 \times .\overline{6}-6 = 16$$

$$6+6+6/6+.\overline{6} \times 6 = 17$$

$$6+6 \times 6-6 \times .\overline{6} \times 6 = 18$$

$$6+6+.6+.6 \times .\overline{6}+6 = 19$$

$$6+6+6+6-.\overline{6} \times 6 = 20$$

$$6+6+6-.6+.6 \times 6 = 21$$

$$6/6-.6+6 \times .6 \times 6 = 22$$

$$6+6+6+6-6/6 = 23$$

$$6+6+6+6+6-6 = 24$$

$$6+6+6+6+6/6 = 25$$

$$6+6 \times 6 \times .\overline{6}-.\overline{6} \times 6 = 26$$

$$6 \times 6+.6-6-.6 \times 6 = 27$$

$$6+6+6+6+.\overline{6} \times 6 = 28$$

$$6+6 \times 6 \times .\overline{6}-6/6 = 29$$

$$6+6+6 \times 6 \times .\overline{6}-6 = 30$$

$$6+6/6+6 \times .\overline{6} \times 6 = 31$$

$$6+6 \times 6-6-.\overline{6} \times 6 = 32$$

$$6+6-.6+6 \times .6 \times 6 = 33$$

$$6+6 \times 6 \times .\overline{6}+.\overline{6} \times 6 = 34$$

$$6+6 \times 6-6-6/6 = 35$$

$$6+6+6+6+6+6 = 36$$

$$6+6/6+6 \times 6-6 = 37$$

$$6/6+6/6+6 \times 6 = 38$$

$$6+6 \times 6+.6-.6 \times 6 = 39$$

$$6+6 \times 6+6 \times .\overline{6}-6 = 40$$

$$6-.6-.6 \times .\overline{6}+6 \times 6 = 41$$

$$6+6+6+6 \times .\overline{6} \times 6 = 42$$

$$6+.6+.6 \times .\overline{6}+6 \times 6 = 43$$

$$6+6+6 \times 6-.\overline{6} \times 6 = 44$$

$$6+6 \times 6-.6+.6 \times 6 = 45$$

$$66 \times .6+.6 \times .\overline{6}+6 = 46$$

$$6+6+6 \times 6-6/6 = 47$$

$$6+6+6+6 \times 6-6 = 48$$

$$6+6+6/6+6 \times 6 = 49$$

$$66-6-6-.\overline{6} \times 6 = 50$$

$$66 \times .6+6-.6+6 = 51$$

$$6+6+6 \times 6+.\overline{6} \times 6 = 52$$

$$66 - 6 - 6 - 6/6 = 53$$

$$6 \times 6+6 \times 6 \times .\overline{6}-6 = 54$$

$$66+6/6-6-6 = 55$$

$$6!!+6!!-6 \times 6-.\overline{6} \times 6 = 56$$

$$6 \times 6-.6+6 \times .6 \times 6 = 57$$

$$66+6 \times .\overline{6}-6-6 = 58$$

$$66-.6-.6 \times .\overline{6}-6 = 59$$

$$6+6+6+6+6 \times 6 = 60$$

$$66+.6+.6 \times .\overline{6}-6 = 61$$

$$66+6-6-.\overline{6} \times 6 = 62$$

$$66+6/6-.\overline{6} \times 6 = 63$$

$$6 \times 6 \times .\overline{6} \times .\overline{6} \times .\overline{6} \times 6 = 64$$

$$66+6-6-6/6 = 65$$

$$6+6 \times 6+6 \times .\overline{6} \times 6 = 66$$

$$66+6+6/6-6 = 67$$

$$6 \times 6+6 \times 6-.\overline{6} \times 6 = 68$$

$$66+6+.6-.6 \times 6 = 69$$

$$66+6+6 \times .\overline{6}-6 = 70$$

$$6 \times 6+6 \times 6-6/6 = 71$$

$$6+6 \times 6+6 \times 6-6 = 72$$

$$6/6+6 \times 6+6 \times 6 = 73$$

$$66+6+6-.\overline{6} \times 6 = 74$$

$$66+6-.6+.6 \times 6 = 75$$

$$6 \times 6+6 \times 6+.\overline{6} \times 6 = 76$$

$$66+6+6-6/6 = 77$$

$$66+6+6+6-6 = 78$$

$$66+6+6+6/6 = 79$$

$$6!!/6+6 \times 6+6 \times 6 = 80$$

$$6!!+6 \times 6+.6-.6 \times 6 = 81$$

$$66+6+6+.\overline{6} \times 6 = 82$$

$$6!/6-6/6-6 \times 6 = 83$$

$$6+6+6 \times 6+6 \times 6 = 84$$

$$6!/6+6/6-6 \times 6 = 85$$

$$66 \times .\overline{6}+6+6 \times 6 = 86$$

$$.6+6 \times 6 \times .6 \times .\overline{6} \times 6 = 87$$

$$6!/6+6 \times .\overline{6}-6 \times 6 = 88$$

$$6!!+6+6 \times 6-6/6 = 89$$

$$6 \times 6 \times 6 \times .\overline{6} \times .\overline{6}-6 = 90$$

$$6!!+6+6/6+6 \times 6 = 91$$

$$6!! \times 6 \times .\overline{6} \times .\overline{6}-6 \times 6 = 92$$

$$6!!+6!!+6/6-.\overline{6} \times 6 = 93$$

$$6!!+6+6 \times 6+.\overline{6} \times 6 = 94$$

$$6!!+6!!+6-6-6/6 = 95$$

$$66+6+6 \times .\overline{6} \times 6 = 96$$

$$6!!+6!!+6+6/6-6 = 97$$

$$66+6 \times 6-.\overline{6} \times 6 = 98$$

$$6!/6+.6-6 \times .6 \times 6 = 99$$

$$6!!+6!!+6+6 \times .\overline{6}-6 = 100$$

• 80: 6!/(6*6) + 6*6/.6 Commented Apr 23, 2020 at 11:02
• $91=6!!+6*6+6+\frac{6}{6}$ Commented Apr 23, 2020 at 11:25
• $100=\frac{666-66}{6}$
– JMP
Commented Apr 23, 2020 at 11:44
• How does 6!! = 48? Does 6!! mean something different from (6!)!? Commented Apr 23, 2020 at 20:43
• @AhmedAbdelhameed Yes, it is a double factorial which is evaluated as $n \cdot (n-2) \dots$. $6!! = 6 \cdot 4 \cdot 2 = 48$. Commented Apr 23, 2020 at 20:46

Some numbers missing from eyl327's answer

$$80=6!/6-6\cdot6-.\bar6\cdot6$$
$$83=6!/6-6\cdot6-6/6$$
$$85=6!/6-6\cdot6+6/6$$
$$88=6!/6-6\cdot6+.\bar6\cdot6$$
$$96=6!/6-6-6-6-6$$