5
$\begingroup$

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.

$\endgroup$
  • 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
  • 2
    $\begingroup$ is factorial allowed? $\endgroup$ – njzk2 Sep 11 '16 at 17:27
1
$\begingroup$

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

$18 = 2+0+16$

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

$19 = 2+0!+16$

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

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

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

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

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

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

You should be able to continue on your own.

$\endgroup$
  • 7
    $\begingroup$ 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
2
$\begingroup$

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

$\endgroup$
4
$\begingroup$
  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. $2^0 + (1 + 6)^2$

$\endgroup$
  • 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
  • 2
    $\begingroup$ exponents larger than 3 are not allowed according to the comments $\endgroup$ – elias Sep 11 '16 at 12:50
11
$\begingroup$

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: $(2+0)*(-1+6)^2$
$\endgroup$
  • $\begingroup$ 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
  • 1
    $\begingroup$ @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

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.