[Guest]

Below given is a blank equation:

____ + ____ = ____

you are given digits 1,2,3,4,5,and 6

Use each only once once without any mathematical operator other than the ones provided in the equation to make this equation true.

Each digit must be used in every solution.

I know of three solutions. Can you provide more?

[Guest]

EDIT: Nevermind, wrong answer...

Edited July 30, 2010 by Anza Power

[Guest]

The only way i figured it could go is

##+##=##

because it can't be #+##=### or any other type of combination, but I've tried all possibilities and none was true:

12+34=56 FALSE

12+34=65 FALSE

12+35=46 FALSE

12+35=64 FALSE

12+36=45 FALSE

12+36=54 FALSE

12+43=56 FALSE

12+43=65 FALSE

12+45=36 FALSE

12+45=63 FALSE

12+46=35 FALSE

12+46=53 FALSE

12+53=46 FALSE

12+53=64 FALSE

12+54=36 FALSE

12+54=63 FALSE

12+56=34 FALSE

12+56=43 FALSE

12+63=45 FALSE

12+63=54 FALSE

12+64=35 FALSE

12+64=53 FALSE

12+65=34 FALSE

12+65=43 FALSE

13+24=56 FALSE

13+24=65 FALSE

13+25=46 FALSE

13+25=64 FALSE

13+26=45 FALSE

13+26=54 FALSE

13+42=56 FALSE

13+42=65 FALSE

13+45=26 FALSE

13+45=62 FALSE

13+46=25 FALSE

13+46=52 FALSE

13+52=46 FALSE

13+52=64 FALSE

13+54=26 FALSE

13+54=62 FALSE

13+56=24 FALSE

13+56=42 FALSE

13+62=45 FALSE

13+62=54 FALSE

13+64=25 FALSE

13+64=52 FALSE

13+65=24 FALSE

13+65=42 FALSE

14+23=56 FALSE

14+23=65 FALSE

14+25=36 FALSE

14+25=63 FALSE

14+26=35 FALSE

14+26=53 FALSE

14+32=56 FALSE

14+32=65 FALSE

14+35=26 FALSE

14+35=62 FALSE

14+36=25 FALSE

14+36=52 FALSE

14+52=36 FALSE

14+52=63 FALSE

14+53=26 FALSE

14+53=62 FALSE

14+56=23 FALSE

14+56=32 FALSE

14+62=35 FALSE

14+62=53 FALSE

14+63=25 FALSE

14+63=52 FALSE

14+65=23 FALSE

14+65=32 FALSE

15+23=46 FALSE

15+23=64 FALSE

15+24=36 FALSE

15+24=63 FALSE

15+26=34 FALSE

15+26=43 FALSE

15+32=46 FALSE

15+32=64 FALSE

15+34=26 FALSE

15+34=62 FALSE

15+36=24 FALSE

15+36=42 FALSE

15+42=36 FALSE

15+42=63 FALSE

15+43=26 FALSE

15+43=62 FALSE

15+46=23 FALSE

15+46=32 FALSE

15+62=34 FALSE

15+62=43 FALSE

15+63=24 FALSE

15+63=42 FALSE

15+64=23 FALSE

15+64=32 FALSE

16+23=45 FALSE

16+23=54 FALSE

16+24=35 FALSE

16+24=53 FALSE

16+25=34 FALSE

16+25=43 FALSE

16+32=45 FALSE

16+32=54 FALSE

16+34=25 FALSE

16+34=52 FALSE

16+35=24 FALSE

16+35=42 FALSE

16+42=35 FALSE

16+42=53 FALSE

16+43=25 FALSE

16+43=52 FALSE

16+45=23 FALSE

16+45=32 FALSE

16+52=34 FALSE

16+52=43 FALSE

16+53=24 FALSE

16+53=42 FALSE

16+54=23 FALSE

16+54=32 FALSE

21+34=56 FALSE

21+34=65 FALSE

21+35=46 FALSE

21+35=64 FALSE

21+36=45 FALSE

21+36=54 FALSE

21+43=56 FALSE

21+43=65 FALSE

21+45=36 FALSE

21+45=63 FALSE

21+46=35 FALSE

21+46=53 FALSE

21+53=46 FALSE

21+53=64 FALSE

21+54=36 FALSE

21+54=63 FALSE

21+56=34 FALSE

21+56=43 FALSE

21+63=45 FALSE

21+63=54 FALSE

21+64=35 FALSE

21+64=53 FALSE

21+65=34 FALSE

21+65=43 FALSE

23+14=56 FALSE

23+14=65 FALSE

23+15=46 FALSE

23+15=64 FALSE

23+16=45 FALSE

23+16=54 FALSE

23+41=56 FALSE

23+41=65 FALSE

23+45=16 FALSE

23+45=61 FALSE

23+46=15 FALSE

23+46=51 FALSE

23+51=46 FALSE

23+51=64 FALSE

23+54=16 FALSE

23+54=61 FALSE

23+56=14 FALSE

23+56=41 FALSE

23+61=45 FALSE

23+61=54 FALSE

23+64=15 FALSE

23+64=51 FALSE

23+65=14 FALSE

23+65=41 FALSE

24+13=56 FALSE

24+13=65 FALSE

24+15=36 FALSE

24+15=63 FALSE

24+16=35 FALSE

24+16=53 FALSE

24+31=56 FALSE

24+31=65 FALSE

24+35=16 FALSE

24+35=61 FALSE

24+36=15 FALSE

24+36=51 FALSE

24+51=36 FALSE

24+51=63 FALSE

24+53=16 FALSE

24+53=61 FALSE

24+56=13 FALSE

24+56=31 FALSE

24+61=35 FALSE

24+61=53 FALSE

24+63=15 FALSE

24+63=51 FALSE

24+65=13 FALSE

24+65=31 FALSE

25+13=46 FALSE

25+13=64 FALSE

25+14=36 FALSE

25+14=63 FALSE

25+16=34 FALSE

25+16=43 FALSE

25+31=46 FALSE

25+31=64 FALSE

25+34=16 FALSE

25+34=61 FALSE

25+36=14 FALSE

25+36=41 FALSE

25+41=36 FALSE

25+41=63 FALSE

25+43=16 FALSE

25+43=61 FALSE

25+46=13 FALSE

25+46=31 FALSE

25+61=34 FALSE

25+61=43 FALSE

25+63=14 FALSE

25+63=41 FALSE

25+64=13 FALSE

25+64=31 FALSE

26+13=45 FALSE

26+13=54 FALSE

26+14=35 FALSE

26+14=53 FALSE

26+15=34 FALSE

26+15=43 FALSE

26+31=45 FALSE

26+31=54 FALSE

26+34=15 FALSE

26+34=51 FALSE

26+35=14 FALSE

26+35=41 FALSE

26+41=35 FALSE

26+41=53 FALSE

26+43=15 FALSE

26+43=51 FALSE

26+45=13 FALSE

26+45=31 FALSE

26+51=34 FALSE

26+51=43 FALSE

26+53=14 FALSE

26+53=41 FALSE

26+54=13 FALSE

26+54=31 FALSE

31+24=56 FALSE

31+24=65 FALSE

31+25=46 FALSE

31+25=64 FALSE

31+26=45 FALSE

31+26=54 FALSE

31+42=56 FALSE

31+42=65 FALSE

31+45=26 FALSE

31+45=62 FALSE

31+46=25 FALSE

31+46=52 FALSE

31+52=46 FALSE

31+52=64 FALSE

31+54=26 FALSE

31+54=62 FALSE

31+56=24 FALSE

31+56=42 FALSE

31+62=45 FALSE

31+62=54 FALSE

31+64=25 FALSE

31+64=52 FALSE

31+65=24 FALSE

31+65=42 FALSE

32+14=56 FALSE

32+14=65 FALSE

32+15=46 FALSE

32+15=64 FALSE

32+16=45 FALSE

32+16=54 FALSE

32+41=56 FALSE

32+41=65 FALSE

32+45=16 FALSE

32+45=61 FALSE

32+46=15 FALSE

32+46=51 FALSE

32+51=46 FALSE

32+51=64 FALSE

32+54=16 FALSE

32+54=61 FALSE

32+56=14 FALSE

32+56=41 FALSE

32+61=45 FALSE

32+61=54 FALSE

32+64=15 FALSE

32+64=51 FALSE

32+65=14 FALSE

32+65=41 FALSE

34+12=56 FALSE

34+12=65 FALSE

34+15=26 FALSE

34+15=62 FALSE

34+16=25 FALSE

34+16=52 FALSE

34+21=56 FALSE

34+21=65 FALSE

34+25=16 FALSE

34+25=61 FALSE

34+26=15 FALSE

34+26=51 FALSE

34+51=26 FALSE

34+51=62 FALSE

34+52=16 FALSE

34+52=61 FALSE

34+56=12 FALSE

34+56=21 FALSE

34+61=25 FALSE

34+61=52 FALSE

34+62=15 FALSE

34+62=51 FALSE

34+65=12 FALSE

34+65=21 FALSE

35+12=46 FALSE

35+12=64 FALSE

35+14=26 FALSE

35+14=62 FALSE

35+16=24 FALSE

35+16=42 FALSE

35+21=46 FALSE

35+21=64 FALSE

35+24=16 FALSE

35+24=61 FALSE

35+26=14 FALSE

35+26=41 FALSE

35+41=26 FALSE

35+41=62 FALSE

35+42=16 FALSE

35+42=61 FALSE

35+46=12 FALSE

35+46=21 FALSE

35+61=24 FALSE

35+61=42 FALSE

35+62=14 FALSE

35+62=41 FALSE

35+64=12 FALSE

35+64=21 FALSE

36+12=45 FALSE

36+12=54 FALSE

36+14=25 FALSE

36+14=52 FALSE

36+15=24 FALSE

36+15=42 FALSE

36+21=45 FALSE

36+21=54 FALSE

36+24=15 FALSE

36+24=51 FALSE

36+25=14 FALSE

36+25=41 FALSE

36+41=25 FALSE

36+41=52 FALSE

36+42=15 FALSE

36+42=51 FALSE

36+45=12 FALSE

36+45=21 FALSE

36+51=24 FALSE

36+51=42 FALSE

36+52=14 FALSE

36+52=41 FALSE

36+54=12 FALSE

36+54=21 FALSE

41+23=56 FALSE

41+23=65 FALSE

41+25=36 FALSE

41+25=63 FALSE

41+26=35 FALSE

41+26=53 FALSE

41+32=56 FALSE

41+32=65 FALSE

41+35=26 FALSE

41+35=62 FALSE

41+36=25 FALSE

41+36=52 FALSE

41+52=36 FALSE

41+52=63 FALSE

41+53=26 FALSE

41+53=62 FALSE

41+56=23 FALSE

41+56=32 FALSE

41+62=35 FALSE

41+62=53 FALSE

41+63=25 FALSE

41+63=52 FALSE

41+65=23 FALSE

41+65=32 FALSE

42+13=56 FALSE

42+13=65 FALSE

42+15=36 FALSE

42+15=63 FALSE

42+16=35 FALSE

42+16=53 FALSE

42+31=56 FALSE

42+31=65 FALSE

42+35=16 FALSE

42+35=61 FALSE

42+36=15 FALSE

42+36=51 FALSE

42+51=36 FALSE

42+51=63 FALSE

42+53=16 FALSE

42+53=61 FALSE

42+56=13 FALSE

42+56=31 FALSE

42+61=35 FALSE

42+61=53 FALSE

42+63=15 FALSE

42+63=51 FALSE

42+65=13 FALSE

42+65=31 FALSE

43+12=56 FALSE

43+12=65 FALSE

43+15=26 FALSE

43+15=62 FALSE

43+16=25 FALSE

43+16=52 FALSE

43+21=56 FALSE

43+21=65 FALSE

43+25=16 FALSE

43+25=61 FALSE

43+26=15 FALSE

43+26=51 FALSE

43+51=26 FALSE

43+51=62 FALSE

43+52=16 FALSE

43+52=61 FALSE

43+56=12 FALSE

43+56=21 FALSE

43+61=25 FALSE

43+61=52 FALSE

43+62=15 FALSE

43+62=51 FALSE

43+65=12 FALSE

43+65=21 FALSE

45+12=36 FALSE

45+12=63 FALSE

45+13=26 FALSE

45+13=62 FALSE

45+16=23 FALSE

45+16=32 FALSE

45+21=36 FALSE

45+21=63 FALSE

45+23=16 FALSE

45+23=61 FALSE

45+26=13 FALSE

45+26=31 FALSE

45+31=26 FALSE

45+31=62 FALSE

45+32=16 FALSE

45+32=61 FALSE

45+36=12 FALSE

45+36=21 FALSE

45+61=23 FALSE

45+61=32 FALSE

45+62=13 FALSE

45+62=31 FALSE

45+63=12 FALSE

45+63=21 FALSE

46+12=35 FALSE

46+12=53 FALSE

46+13=25 FALSE

46+13=52 FALSE

46+15=23 FALSE

46+15=32 FALSE

46+21=35 FALSE

46+21=53 FALSE

46+23=15 FALSE

46+23=51 FALSE

46+25=13 FALSE

46+25=31 FALSE

46+31=25 FALSE

46+31=52 FALSE

46+32=15 FALSE

46+32=51 FALSE

46+35=12 FALSE

46+35=21 FALSE

46+51=23 FALSE

46+51=32 FALSE

46+52=13 FALSE

46+52=31 FALSE

46+53=12 FALSE

46+53=21 FALSE

51+23=46 FALSE

51+23=64 FALSE

51+24=36 FALSE

51+24=63 FALSE

51+26=34 FALSE

51+26=43 FALSE

51+32=46 FALSE

51+32=64 FALSE

51+34=26 FALSE

51+34=62 FALSE

51+36=24 FALSE

51+36=42 FALSE

51+42=36 FALSE

51+42=63 FALSE

51+43=26 FALSE

51+43=62 FALSE

51+46=23 FALSE

51+46=32 FALSE

51+62=34 FALSE

51+62=43 FALSE

51+63=24 FALSE

51+63=42 FALSE

51+64=23 FALSE

51+64=32 FALSE

52+13=46 FALSE

52+13=64 FALSE

52+14=36 FALSE

52+14=63 FALSE

52+16=34 FALSE

52+16=43 FALSE

52+31=46 FALSE

52+31=64 FALSE

52+34=16 FALSE

52+34=61 FALSE

52+36=14 FALSE

52+36=41 FALSE

52+41=36 FALSE

52+41=63 FALSE

52+43=16 FALSE

52+43=61 FALSE

52+46=13 FALSE

52+46=31 FALSE

52+61=34 FALSE

52+61=43 FALSE

52+63=14 FALSE

52+63=41 FALSE

52+64=13 FALSE

52+64=31 FALSE

53+12=46 FALSE

53+12=64 FALSE

53+14=26 FALSE

53+14=62 FALSE

53+16=24 FALSE

53+16=42 FALSE

53+21=46 FALSE

53+21=64 FALSE

53+24=16 FALSE

53+24=61 FALSE

53+26=14 FALSE

53+26=41 FALSE

53+41=26 FALSE

53+41=62 FALSE

53+42=16 FALSE

53+42=61 FALSE

53+46=12 FALSE

53+46=21 FALSE

53+61=24 FALSE

53+61=42 FALSE

53+62=14 FALSE

53+62=41 FALSE

53+64=12 FALSE

53+64=21 FALSE

54+12=36 FALSE

54+12=63 FALSE

54+13=26 FALSE

54+13=62 FALSE

54+16=23 FALSE

54+16=32 FALSE

54+21=36 FALSE

54+21=63 FALSE

54+23=16 FALSE

54+23=61 FALSE

54+26=13 FALSE

54+26=31 FALSE

54+31=26 FALSE

54+31=62 FALSE

54+32=16 FALSE

54+32=61 FALSE

54+36=12 FALSE

54+36=21 FALSE

54+61=23 FALSE

54+61=32 FALSE

54+62=13 FALSE

54+62=31 FALSE

54+63=12 FALSE

54+63=21 FALSE

56+12=34 FALSE

56+12=43 FALSE

56+13=24 FALSE

56+13=42 FALSE

56+14=23 FALSE

56+14=32 FALSE

56+21=34 FALSE

56+21=43 FALSE

56+23=14 FALSE

56+23=41 FALSE

56+24=13 FALSE

56+24=31 FALSE

56+31=24 FALSE

56+31=42 FALSE

56+32=14 FALSE

56+32=41 FALSE

56+34=12 FALSE

56+34=21 FALSE

56+41=23 FALSE

56+41=32 FALSE

56+42=13 FALSE

56+42=31 FALSE

56+43=12 FALSE

56+43=21 FALSE

61+23=45 FALSE

61+23=54 FALSE

61+24=35 FALSE

61+24=53 FALSE

61+25=34 FALSE

61+25=43 FALSE

61+32=45 FALSE

61+32=54 FALSE

61+34=25 FALSE

61+34=52 FALSE

61+35=24 FALSE

61+35=42 FALSE

61+42=35 FALSE

61+42=53 FALSE

61+43=25 FALSE

61+43=52 FALSE

61+45=23 FALSE

61+45=32 FALSE

61+52=34 FALSE

61+52=43 FALSE

61+53=24 FALSE

61+53=42 FALSE

61+54=23 FALSE

61+54=32 FALSE

62+13=45 FALSE

62+13=54 FALSE

62+14=35 FALSE

62+14=53 FALSE

62+15=34 FALSE

62+15=43 FALSE

62+31=45 FALSE

62+31=54 FALSE

62+34=15 FALSE

62+34=51 FALSE

62+35=14 FALSE

62+35=41 FALSE

62+41=35 FALSE

62+41=53 FALSE

62+43=15 FALSE

62+43=51 FALSE

62+45=13 FALSE

62+45=31 FALSE

62+51=34 FALSE

62+51=43 FALSE

62+53=14 FALSE

62+53=41 FALSE

62+54=13 FALSE

62+54=31 FALSE

63+12=45 FALSE

63+12=54 FALSE

63+14=25 FALSE

63+14=52 FALSE

63+15=24 FALSE

63+15=42 FALSE

63+21=45 FALSE

63+21=54 FALSE

63+24=15 FALSE

63+24=51 FALSE

63+25=14 FALSE

63+25=41 FALSE

63+41=25 FALSE

63+41=52 FALSE

63+42=15 FALSE

63+42=51 FALSE

63+45=12 FALSE

63+45=21 FALSE

63+51=24 FALSE

63+51=42 FALSE

63+52=14 FALSE

63+52=41 FALSE

63+54=12 FALSE

63+54=21 FALSE

64+12=35 FALSE

64+12=53 FALSE

64+13=25 FALSE

64+13=52 FALSE

64+15=23 FALSE

64+15=32 FALSE

64+21=35 FALSE

64+21=53 FALSE

64+23=15 FALSE

64+23=51 FALSE

64+25=13 FALSE

64+25=31 FALSE

64+31=25 FALSE

64+31=52 FALSE

64+32=15 FALSE

64+32=51 FALSE

64+35=12 FALSE

64+35=21 FALSE

64+51=23 FALSE

64+51=32 FALSE

64+52=13 FALSE

64+52=31 FALSE

64+53=12 FALSE

64+53=21 FALSE

65+12=34 FALSE

65+12=43 FALSE

65+13=24 FALSE

65+13=42 FALSE

65+14=23 FALSE

65+14=32 FALSE

65+21=34 FALSE

65+21=43 FALSE

65+23=14 FALSE

65+23=41 FALSE

65+24=13 FALSE

65+24=31 FALSE

65+31=24 FALSE

65+31=42 FALSE

65+32=14 FALSE

65+32=41 FALSE

65+34=12 FALSE

65+34=21 FALSE

65+41=23 FALSE

65+41=32 FALSE

65+42=13 FALSE

65+42=31 FALSE

65+43=12 FALSE

65+43=21 FALSE

Could we use fractions or dots here? (i.e 16/4, 3.2)

[Guest]

Fractions are not allowed. But you can use the digits in some other manner

[Guest]

4^3 + 1^2 = 65

If you write it in classic mathematical manner, you don't need to use '^' which is used for programming.

[Guest]

4^3 + 1^2 = 65

If you write it in classic mathematical manner, you don't need to use '^' which is used for programming.

One correct ..two more to go

[Guest]

2^5 + 4^1 = 36

[Guest]

2^5 + 4^1 = 36

one more to go

[Guest]

Most of them involve 1 raised to any power is still 1

1^234+5=6

1^236+4=5

1^243+5=6

1^2+4^3=65

1^256+3=4

1^263+4=5

1^265+3=4

1^324+5=6

1^326+4=5

1^342+5=6

1^362+4=5

1^423+5=6

1^432+5=6

1^4+35=6^2

1^456+2=3

1^465+2=3

1^526+3=4

1^546+2=3

1^562+3=4

1^564+2=3

1^623+4=5

1^625+3=4

1^632+4=5

1^645+2=3

1^652+3=4

1^654+2=3

2^5+4^1=36

2^5+4=36^1

35+1^4=6^2

4^1+2^5=36

4^3+1^2=65

[Guest]

Well i'm stumped.

Every possible combination and didn't get anything.

I'm thinking that we need to switch to a different base to make the equation true. Base 6? I'll have to get back to this one.

[Guest]

Below given is a blank equation:

____ + ____ = ____

you are given digits 1,2,3,4,5,and 6

Use each only once once without any mathematical operator other than the ones provided in the equation to make this equation true.

Each digit must be used in every solution.

I know of three solutions. Can you provide more?

Isn't raising a number to a power (i.e., exponents) a mathematical operation, too? Yet, you say not other mathematical operations, and even say that fractions aren't allowed. Maybe I'm just too new, but this is confusing.

[Guest]

Isn't raising a number to a power (i.e., exponents) a mathematical operation, too? Yet, you say not other mathematical operations, and even say that fractions aren't allowed. Maybe I'm just too new, but this is confusing.

I think it's because you don't need to write an operator, just the exponent. It's a little confusing, but I guess that was his intention. He wrote "operator" and we assumed "operation".

[Guest]

4^(1+3)=256

I think i have it

[Guest]

You need to change the base.

14+36=52 Base 8

15+26=43 Base 8

16+25=43 Base 8

16+34=52 Base 8

24+35=61 Base 8

25+16=43 Base 8

25+34=61 Base 8

26+15=43 Base 8

34+16=52 Base 8

34+25=61 Base 8

35+24=61 Base 8

36+14=52 Base 8

I tried a bunch of other bases, and base 8 is the only one that works.

[Guest]

One correct ..two more to go

You told not to use any mathematical operator than + and == so ^ is also a mathematical operastor. Isnt it?

Edited July 31, 2010 by parik

[Guest]

You told not to use any mathematical operator than + and == so ^ is also a mathematical operastor. Isnt it?

you are considering this operator thing too seriously..this is just rearranging the digits in another manner

[Guest]

Solved by Hugo and others