# Making 1-50 from 2016

Make the numbers 1-50 using the numbers 2 0 1 6 in the given order.

1.You must use all four digits.

2.You may not use any other numbers.

3.You may use +, -, x, ÷, square root, squaring and cubing, exponentiation, parentheses, brackets, or other grouping symbols.

• What operations are allowed? – Matsmath Sep 11 '16 at 11:28
• All operations are allowed – NotVeryGood Sep 11 '16 at 11:38
• Can you form two-digit numbers, e.g. 20+16=36? Please edit your question accordingly. – Matsmath Sep 11 '16 at 11:39
• @Matsmath I've editted it – NotVeryGood Sep 11 '16 at 11:43
• is factorial allowed? – njzk2 Sep 11 '16 at 17:27

Here's the complete list from 1 to 50. Some of them can be done in a 'pure' way, with no numbers appearing in the expression except the four specified. Others require squaring or cubing (which the OP said is permitted), and I've marked these as such.

1. $2*0+1^6$
2. $2+0*16$
3. $2+0+1^6$
4. $20-16$
5. $2*0-1+6$
6. $2*0*1+6$
7. $2*0+1+6$
8. $2+0*1+6$
9. $2+0+1+6$
10. $2*(0-1+6)$
11. Needs squaring/cubing: $2^2+0+1+6$
12. $2*(0*1+6)$
13. $20-1-6$
14. $20*1-6$
15. $20+1-6$
16. $2*0+16$
17. $2^0+16$
18. $2+0+16$
19. $20-1^6$
20. $20/1^6$
21. $20+1^6$
22. $20+\sqrt{\sqrt{16}}$ (thanks @MariaDeleva)
23. Needs squaring/cubing: $-2+0+(-1+6)^2$
24. $20+\sqrt{16}$
25. $20-1+6$
26. $20*1+6$
27. $20+1+6$
28. Needs squaring/cubing: $-2^3+0*1+6^2$
29. Needs squaring/cubing: $-2^3+0+1+6^2$
30. Needs squaring/cubing: $(2^2+0+1)*6$
31. Needs squaring/cubing: $-2^2+0-1+6^2$
32. $(2+0)*16$
33. Needs squaring/cubing: $-2^2-0+1+6^2$
34. Needs squaring/cubing: $-2+0*1+6^2$
35. Needs squaring/cubing: $-2-0+1+6^2$
36. $20+16$
37. Needs squaring/cubing: $2-0-1+6^2$
38. Needs squaring/cubing: $2+0*1+6^2$
39. Needs squaring/cubing: $2+0+1+6^2$
40. $20*\sqrt{\sqrt{16}}$
41. Needs squaring/cubing: $2^2+0+1+6^2$
42. Needs squaring/cubing: $(2^3-0-1)*6$
43. Needs squaring/cubing: $2^3-0-1+6^2$
44. Needs squaring/cubing: $2^3+0*1+6^2$
45. Needs squaring/cubing: $2^3+0+1+6^2$
46. Needs factorial? $2^3+0!+1+6^2$ (thanks @numberknot)
47. Needs squaring/cubing: $-2-0+(1+6)^2$
48. Needs squaring/cubing: $(2^3+0*1)*6$
49. Needs squaring/cubing: $2*0+(1+6)^2$
50. Needs squaring/cubing: $(2+0)*(-1+6)^2$
• That was quick, even if you only got half! – Beastly Gerbil Sep 11 '16 at 12:05
• Thank you for these even if its only half ^3^ – NotVeryGood Sep 11 '16 at 12:08
• 46=2^3+0!+1+6^2 – Numberknot Sep 11 '16 at 13:02
• @numberknot Is factorial allowed? It's not one of the operations mentioned in the question. – Rand al'Thor Sep 11 '16 at 13:03
• @NotVeryGood The list is complete! :-) – Rand al'Thor Sep 11 '16 at 13:33
1. $2 * 0 + 1 ^ 6$

2. $2 + 0 * 1 * 6$

3. $2 + 0 + 1 ^ 6$

4. $20 - 16$

5. $2 * 0 + 1 - 6$

6. $2 * 0 * 1 + 6$

7. $2 * 0 + 1 + 6$

8. $2 + 0 * 1 + 6$

9. $2 + 0 + 1 + 6$

10. $2 * (0 - 1 + 6)$

11. $2 ^ 2 + 0 + 1 + 6$

12. $(2 + (0 * 1)) * 6$

13. $20 - 1 - 6$

14. $20 - 1*6$

15. $20 + 1 - 6$

16. $2 * 0 + 16$

17. $2 ^ 0 + 16$

18. $(2 + 0 + 1) * 6$

19. $20 - (1 ^ 6)$

20. $20/1 ^ 6$

21. $20 + 1 ^ 6$

22. $20 + \sqrt{\sqrt{16}}$ (Credits Maria Deleva)

23. $-2 + 0 + (-1 + 6)^2$

24. $20 + \sqrt{16}$

25. $20 - 1 + 6$

26. $20 + 1 * 6$

27. $20 + 1 + 6$

28. $(2 ^ 2 + 0) * (1 + 6)$

29. $-(2 ^ 3) + 0 + 1 + 6 ^ 2$

30. $(2 ^ 2 + 0 + 1) * 6$

31. $(2 ^ 2 + 0 + 1)^2 + 6$

32. $(2 + 0) * 16$

33. $-(2 + 0 + 1) + 6 ^ 2$

34. $-2 + 0 * 1 + 6 ^ 2$

35. $2 * 0 - 1 + 6 ^ 2$

36. $20 + 16$

37. $2 + 0 - 1 + 6 ^ 2$

38. $2 + 0 * 1 + 6 ^ 2$

39. $2 + 0 + 1 + 6 ^ 2$

40. $20 * \sqrt{\sqrt{16}}$

41. $2 ^ 2 + 0 + 1 + 6 ^ 2$

42. $(2 ^ 3 + 0 - 1) * 6$

43. $2 ^ 3 + 0 - 1 + 6 ^ 2$

44. $2 ^ 3 + 0 * 1 + 6 ^ 2$

45. $2 ^ 3 + 0 + 1 + 6 ^ 2$

46. $-2 + 0 + (1 + 6)^2$

47. $(2 ^ 3 + 0 * 1) * 6$

48. $(2 + 0 - 1 + 6) ^ 2$

49. $2^0 + (1 + 6)^2$

• dude you used digit 3 ..in some of your equation – Numberknot Sep 11 '16 at 12:42
• @numberknot Check the comments – Laschet Jain Sep 11 '16 at 12:45
• exponents larger than 3 are not allowed according to the comments – elias Sep 11 '16 at 12:50

Some of these become possible with decimal point: $$\begin{matrix} 11=.2^{0-1}+6 \\ 30=.2^{0-1}*6 \\ 35=\dfrac{20+1}{.6} \\ 50=\dfrac{20}{1-.6} \end{matrix}$$

$17 = (2*0)!+16$

$18 = 2+0+16$

$18 = (2+0+1)*6$

$19 = 2+0!+16$

$20 = (2+0!+1)!/6$

$21 = (2+0!)(1+6)$

$22 = (2+0!)!+16$

$23 = 2^3-0!+16$

$24 = (2+0!+1)*6$

$25 = (2-0-1-6)^2$

You should be able to continue on your own.

• what's the actual pattern that allows us to continue on our own? – elias Sep 11 '16 at 12:47
• When I answered the question it was different. I was just giving a little hint since he had just gotten stuck at #17. I stopped because it's his homework and it's tedious work. – Machining Machine Sep 11 '16 at 12:51