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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.

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  • 2
    $\begingroup$ What operations are allowed? $\endgroup$ – Matsmath Sep 11 '16 at 11:28
  • $\begingroup$ All operations are allowed $\endgroup$ – NotVeryGood Sep 11 '16 at 11:38
  • $\begingroup$ Can you form two-digit numbers, e.g. 20+16=36? Please edit your question accordingly. $\endgroup$ – Matsmath Sep 11 '16 at 11:39
  • $\begingroup$ @Matsmath I've editted it $\endgroup$ – NotVeryGood Sep 11 '16 at 11:43
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    $\begingroup$ is factorial allowed? $\endgroup$ – njzk2 Sep 11 '16 at 17:27
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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: $(2+0)*(-1+6)^2$
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  • $\begingroup$ That was quick, even if you only got half! $\endgroup$ – Beastly Gerbil Sep 11 '16 at 12:05
  • $\begingroup$ Thank you for these even if its only half ^3^ $\endgroup$ – NotVeryGood Sep 11 '16 at 12:08
  • $\begingroup$ 46=2^3+0!+1+6^2 $\endgroup$ – Numberknot Sep 11 '16 at 13:02
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    $\begingroup$ @numberknot Is factorial allowed? It's not one of the operations mentioned in the question. $\endgroup$ – Rand al'Thor Sep 11 '16 at 13:03
  • $\begingroup$ @NotVeryGood The list is complete! :-) $\endgroup$ – Rand al'Thor Sep 11 '16 at 13:33
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  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. $2 ^ 3 + 0 + 1 + 6 ^ 2$

  47. $-2 + 0 + (1 + 6)^2$

  48. $(2 ^ 3 + 0 * 1) * 6$

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

  50. $2^0 + (1 + 6)^2$

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  • 1
    $\begingroup$ dude you used digit 3 ..in some of your equation $\endgroup$ – Numberknot Sep 11 '16 at 12:42
  • $\begingroup$ @numberknot Check the comments $\endgroup$ – Laschet Jain Sep 11 '16 at 12:45
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    $\begingroup$ exponents larger than 3 are not allowed according to the comments $\endgroup$ – elias Sep 11 '16 at 12:50
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Some of these become possible with decimal point: $$\begin{matrix} 11=.2^{0-1}+6 \\ 30=.2^{0-1}*6 \\ 35=\dfrac{20+1}{.6} \\ 50=\dfrac{20}{1-.6} \end{matrix}$$

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

$18 = 2+0+16$

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

$19 = 2+0!+16$

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

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

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

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

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

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

You should be able to continue on your own.

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    $\begingroup$ what's the actual pattern that allows us to continue on our own? $\endgroup$ – elias Sep 11 '16 at 12:47
  • $\begingroup$ 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. $\endgroup$ – Machining Machine Sep 11 '16 at 12:51

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