1
$\begingroup$

This is very similar to the 2, 0, 1, 8 problem. Just try to make all numbers 1-30 using the digits 2, 0, 1, 9.

Rules:

  • Use all four digits exactly once
  • Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root
  • Parentheses and concatenation are allowed (e.g. $20 + (1 * 9)$)
  • Squaring uses the digit 2 so expressions using multiple twos, like 22 or $12+92$, are not allowed
  • Keep the order "2 0 1 9" in all expressions
  • The modulus operator is not allowed
  • Rounding is not allowed (e.g. $201/9=22$)
|improve this question
$\endgroup$
  • 48
    $\begingroup$ but.. but... how could you? we are not in 2019 yet! $\endgroup$ – Kepotx Apr 17 '18 at 17:07
  • $\begingroup$ Is "0 1 9 2" still considered in to be in order? $\endgroup$ – infinitezero Apr 17 '18 at 18:55
  • $\begingroup$ @infinitezero no $\endgroup$ – jkl3699 Apr 17 '18 at 19:19
  • $\begingroup$ If squaring uses the two, why would square root not use both the one and the two? $\endgroup$ – T James Apr 17 '18 at 22:17
  • 14
    $\begingroup$ Just for fun, $(-2^{-(0!)})!^{-1+\sqrt9}=\pi$, if you use the gamma function for the factorial $\endgroup$ – LegionMammal978 Apr 17 '18 at 23:24
15
$\begingroup$

$30 = 20 + 1 + 9$
$29 = 20^1 + 9$
$28 = 20 - 1 + 9$
$27 =( 2 + 0 + 1)* 9$
$26 = 2 + 0 + (1 + \sqrt{9})!$
$25 = 2^0 + (1 + \sqrt{9})!$
$24 = (2 + 0 - 1 + \sqrt{9})!$
$23 = -2^0 + (1 + \sqrt{9})!$
$22 = -2 + 0 + (1 + \sqrt{9})!$
$21 = 2 + 0 + 19$
$20 = (2 + 0)(1 + 9)$
$19 = 20 - 1^9$
$18 = 2^{(0+1)} * 9$
$17 = -2 + 0 + 19$
$16 = 20 - (1 + \sqrt{9})$
$15 = (2 + 0 + 1)! + 9$
$14 = 20^1 - (\sqrt{9})!$
$13 = 20 - 1 - (\sqrt{9})!$
$12 = 2 + 0 + 1 + 9$
$11 = 2^{(0 + 1)} + 9$
$10 = 2 + 0 - (1 - 9)$
$9 = (2 + 0 + 1)! + \sqrt{9}$
$8 = (2 + 0)(1 + \sqrt{9})$
$7 = -2^{(0 + 1)} + 9$
$6 = 2 + 0 + 1 + \sqrt{9}$
$5 = 2^0 + 1 + \sqrt{9}$
$4 = 2 + 0 - 1 + \sqrt{9}$
$3 = (2 + 0 - 1) * \sqrt{9}$
$2 = (2 + 0) * 1^9$
$1 = (2 - 0 - 1)^9$

|improve this answer
$\endgroup$
  • $\begingroup$ There is also (2^0)*1*9 for nine $\endgroup$ – MEE the sneaky user Apr 18 '18 at 13:54
11
$\begingroup$

$1 = 20 - 19 $
$2 = 2 + 0 * 1 * 9$
$3 = 2 + 0 + 1^9$
$4 = 2 + 0! + 1^9$
$5 = (2 + 0!)! - 1^9$
$6 = (2 + 0 + 1^9)!$
$7 = (2 + 0!)! + 1^9$
$8 = 2 * 0 - 1 + 9$
$9 = 2 * 0 * 1 + 9$
$10 = 2 * 0 + 1 + 9$
$11 = 2 + 0 * 1 +9$
$12 = 2 * 0! + 1 + 9$
$13 = 2 * (0! + 1) + 9$
$14 = (2+0!)!-1+9$
$15 = (2+0!)!+1*9$
$16 = (2+0!)!+1+9$
$17 = 20-\sqrt{1*9}$
$18 = 2 * 0! * 1 *9$
$19 = 20 - 1^9$
$20 = 20 * 1^9$
$21 = 20 + 1^9$
$22 = 20 - 1 + \sqrt{9}$
$23 = 20 + \sqrt{1 * 9}$
$24 = (2 + 0! + 1^9)!$
$25 = 20 -1 + \sqrt{9}!$
$26 = 20 + \sqrt{1 * 9}!$
$27 = (2 + 0 + 1) * 9$
$28 = 20 - 1 + 9$
$29 = 20^1 + 9$
$30 = 20 + 1 + 9 $

|improve this answer
$\endgroup$
3
$\begingroup$

PARTIAL:

19:

$2*0+19$

21:

$2+0+19$

29:

$20+1*9$

30:

$20+1+9$

more incoming

|improve this answer
$\endgroup$
3
$\begingroup$

00

$2 * 0 * 1 * 9$

01

$2 * 0 + 1^9$

02

$2 + 0 * 1 * 9$

03

$2 + 0 + 1 ^ 9$

04

$2 * 0 + 1 + \sqrt{9}$

05

$2 + 0 * 1 + \sqrt{9}$

06

$2 + 0 + 1 + \sqrt{9}$

07

$(20 + 1) / \sqrt{9}$

08

$2 * 0 + ( -1 + 9)$

09

$2 * 0 * 1 + 9$

10

$2 * 0 + 1 + 9$

11

$2 + 0 * 1 + 9$

12

$2 + 0 + 1 + 9$

13

$ 20 - 1 - \sqrt{9}!$

14

2$0 - 1 * \sqrt{9}!$

15

$20 + 1 - \sqrt{9}!$

16

$20 - 1 - \sqrt{9}$

17

$-2 + 0 + 19$

18

$-(2^0) + 19$

19

$2 * 0 + 19$

20

$2 ^ 0 + 19$

21

$2 + 0 + 19$

22

$20 - 1 + \sqrt{9}$

23

$20 + 1 * \sqrt{9}$

24

$20 + 1 + \sqrt{9}$

25

$20 - 1 + \sqrt{9}!$

26

$20 + 1 * \sqrt{9}!$

27

$20 + 1 + \sqrt{9}!$

28

$20 - 1 + 9$

29

$ 20 + 1 * 9$

30

$20 + 1 + 9$

|improve this answer
$\endgroup$
3
$\begingroup$

  1. 20 - 19 = 1
    OR
    SQRT(20 - 19) = 1
    OR
    (20 - 19)! = 1

  2. 2 + 0 * 19 = 2
    OR
    20 / (1 + 9) = 2

  3. 2 + 0 + 1^9 = 3

  4. 2 * 0 + 1 + SQRT(9) = 4

  5. 2 + 0 * 1 + SQRT(9) = 5

  6. - 2 + 0 - 1 + 9 = 6
    OR
    2 + 0 + 1 + SQRT(9) = 6

  7. - 2 + 0 * 1 + 9 = 7
    OR (20 + 1) / SQRT(9) = 7

  8. 2 * 0 - 1 + 9 = 8

  9. 2 * 0 * 1 + 9 = 9
    OR
    2^0 - 1 + 9 = 9

  10. 20 - 1 - 9 = 10
    OR
    20 - (1 + 9) = 10
    OR
    2 * 0 + 1 + 9 = 10

  11. 2 + 0 * 1 + 9 = 11
    OR
    20^1 - 9 = 11
    OR
    2 * 01 + 9 = 11
    OR
    20 * 1 - 9 = 11

  12. 20 + 1 - 9 = 12
    OR
    2 + 0 + 1 + 9 = 12
    OR
    2 - 0 + 1 + 9 = 12

  13. 20 - 1 - (SQRT(9))! = 13

  14. 20 - 1 * (SQRT(9))! = 14

  15. 20 + 1 - (SQRT(9))! = 15

  16. 20 - 1 - SQRT(9) = 16
    OR
    20 - (1 + SQRT(9)) = 16

  17. 20 - 1 * SQRT(9) = 17

  18. 20 + 1 - SQRT(9) = 18
    OR
    (2 + 0) * 1 * 9 = 18
    OR
    (2 + 0) / (1 / 9) = 18

  19. 2 * 0 + 19 = 19

  20. 2^0 + 19 = 20

  21. 2 + 0 + 19 = 21

  22. 20 - 1 + SQRT(9) = 22

  23. 20 * 1 + SQRT(9) = 23

  24. 20 + 1 + SQRT(9) = 24

  25. 20 - 1 + (SQRT(9))! = 25

  26. 20^1 + (SQRT(9))! = 26

  27. 20 + 1 + (SQRT(9))! = 27

  28. 20 - 1 + 9 = 28

  29. 20 * 1 + 9 = 29

  30. 20 + 1 + 9 = 30

|improve this answer
$\endgroup$
  • $\begingroup$ I really like how you gave "or" options. That said, you missed a few more that make 10. $\endgroup$ – sirjonsnow Apr 18 '18 at 14:11
  • $\begingroup$ The ORs were as I found them, and not intended to be a complete solution. I have added a few for 10. $\endgroup$ – NetJohn Apr 18 '18 at 15:17
2
$\begingroup$

Here they are, as simple and neat as I could make them!

$1-6:$

$$\small\begin{array}{c|c}1&2&3&4&5&6\\\hline2\cdot0+1^9&2+0\cdot1\cdot9&2\cdot0\cdot1+\sqrt9&2+0!+1^9&-2-0!-1+9&-2+0-1+9\end{array}$$

$7-12:$

$$\small\begin{array}{c|c}7&8&9&10&11&12\\\hline-2+0\cdot1+9&-2+0+1+9&2\cdot0\cdot1+9&2+0-1+9&2+0\cdot1+9&2+0+1+9\end{array}$$

$13-18:$

$$\small\begin{array}{c|c}13&14&15&16&17&18\\\hline2+0!+1+9&(2+0!)!-1+9&20+1-\sqrt9!&(2+0!)!+1+9&-2+0+19&2\cdot(0+1)\cdot9\end{array}$$

$19-25:$

$$\small\begin{array}{c|c}19&20&21&22&23&24&25\\\hline2\cdot0+19&2^0+19&20+1^9&2+0!+19&20\cdot1+\sqrt9&20+1+\sqrt9&(2+0!)!+19\end{array}$$

$26-30:$

$$\small\begin{array}{c|c}26&27&28&29&30\\\hline20+1\cdot\sqrt9!&20+1+\sqrt9!&20-1+9&20\cdot1+9&20+1+9\end{array}$$

|improve this answer
$\endgroup$
  • $\begingroup$ @Warlord099 Sorted! $\endgroup$ – TheSimpliFire Apr 17 '18 at 19:48
2
$\begingroup$

Full solution

$20-19 = 1 $
$2 + 0 * 19 = 2 $
$2 * 0 * 1 + \sqrt{9} = 3 $
$2 * 0 + 1 + \sqrt{9} = 4$
$2 + 0 * 1 + \sqrt{9} = 5$
$-2 + 0 - 1 + 9 = 6$
$-2 + 0 * 1 + 9 = 7$
$2 * 0 - 1 + 9 = 8$
$2 * 0 * 1 + 9 = 9$
$20 - 1 - 9 = 10$
$20^1 - 9 = 11$
$20 + 1 - 9 = 12$
$20 - 1 - (\sqrt{9})! = 13$
$2 * (0 + 1 + (\sqrt{9})! = 14$
$(2 + 0 + 1)! + 9 = 15$
$2 * (0 - 1 + 9) = 16$
$-2 + 0 + 19 = 17$
$-2^0 + 19 = 18$
$2 * 0 + 19 = 19$
$20! / 19! = 20$
$2 + 0 + 19 = 21$
$20 - 1 + \sqrt{9} = 22$
$20 * 1 + \sqrt{9} = 23$
$20 + 1 + \sqrt{9} = 24$
$20 - 1 + (\sqrt{9})! = 25$
$20 + 1 * (\sqrt{9})! = 26$
$(2 + 0 + 1) * 9 = 27$
$20 - 1 + 9 = 28$
$20 ^1 + 9 = 29$
$20 + 1 + 9 = 30$

|improve this answer
$\endgroup$
2
$\begingroup$

1

$20-19$

2

$2+(0*19)$

3

$(2*0*1)+√9$

4

$(2*0)+√(9)+1$

5

$2+(0*1)+√(9)$

6

$2+0+1+√(9)$

7

$-2+0+(1*9)$

8

$(2*0)-1+9$

9

$(2*0*1)+9$

10

$(2*0)+1+9$

11

$2+(0*1)+9$

12

$2+0+1+9$

13

$20-1-(√9)!$

14

$20*1-(√9)!$

15

$(2+0+1)!+9$

16

$2^(0+1+√9)$

17

$20-(1*√9)$

18

$(2+0*1)*9$

19

$(2*0)+19$

20

$(2^0)+19$

21

$2+0+19$

22

$20-1+√9$

23

$(20*1)+√9$

24

$20+1+√9$

25

$20-1+(√9)!$

26

$(20*1)+(√9)!$

27

$(2+0+1)*9$

28

$20-1+9$

29

$(20*1)+9$

30

$20+1+9$

|improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.