Solve Puzzles

Hai friends,

When puzzles of this type put on, how effecinetly solve them insted of trying 100's of patters and wasting time :confused:

example

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Question:Using 1 through 9 in order, and using only addition or subtraction, create an equation that equals 100.

<Note:I have 10kinds of answers for this>

i.e:. Look at the following example:
Notice that the digits 1 through 9 are used in order to arrive at 106.
1 + 23 - 4 + 5 - 6 + 78 + 9 = 106

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1+2+3-4+5+6+78+9=100
1+2+34-5+67-8+9=100
1+23-4+5+6+78-9=100
1+23-4+56+7+8+9=100
12+3+4+5-6-7+89=100
12-3-4+5-6+7+89=100
123+4-5+67-89=100
123-4-5-6-7+8-9=100
123-45-67+89=100
12+3-4+5+67+8+9 = 100

dclamp,
Great!

But, i did not expect the answer here :D
Just want to no how to approach to solve it :D

how many attempts you tried neally?

zero. Google is my fran

Try working backwards... takes a few attempts.

Who the hell is Fran?

Well he doesn't have a girlfriend, per se, but google shows him lots of dirty pictures so it's close enough :afrog:

Between each digit you can have one of three things:
"+"
or
"-"
or
""

So that gives you 6561 possible equations, the vast majority of which do not equal 100.

Brute forcing this would be the easiest algorithm but the execution time would be terribly slow. It would be exponentially computationally expensive if you used a larger radix (hexadecimal or base32 etc).

Depends if you want to find ANY single correct answer or ALL correct answers.

You could always use a Genetic Algorithm or a Monte Carlo method, those would both certainly be very efficient for this puzzle if the radix is not specified before-hand.

Quote:

---

Originally Posted by wossname

Between each digit you can have one of three things:
"+"
or
"-"
or
""

So that gives you 6561 possible equations, the vast majority of which do not equal 100.

Brute forcing this would be the easiest algorithm but the execution time would be terribly slow. It would be exponentially computationally expensive if you used a larger radix (hexadecimal or base32 etc).

Depends if you want to find ANY single correct answer or ALL correct answers.

You could always use a Genetic Algorithm or a Monte Carlo method, those would both certainly be very efficient for this puzzle if the radix is not specified before-hand.

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Thans wossi for the explanation :thumb:

12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
12345679 * 36 = 444444444
12345679 * 45 = 555555555
12345679 * 54 = 666666666
12345679 * 63 = 777777777
12345679 * 72 = 888888888
12345679 * 81 = 999999999

Quote:

---

Originally Posted by MartinLiss

12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
12345679 * 36 = 444444444
12345679 * 45 = 555555555
12345679 * 54 = 666666666
12345679 * 63 = 777777777
12345679 * 72 = 888888888
12345679 * 81 = 999999999

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oh cool :thumb:

This BASH command will give you the equations that match...

Code:

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for i in {"1+","1-","1"}{"2+","2-","2"}{"3+","3-","3"}{"4+","4-","4"}{"5+","5-","5"}{"6+","6-","6"}{"7+","7-","7"}{"8+","8-","8"}"9"; do echo "$i = $[i]"; done | grep " = 100$"

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Try doing that in MSDOS :D

Quote:

---

Originally Posted by wossname

This BASH command will give you the equations that match...

Code:

---

for i in {"1+","1-","1"}{"2+","2-","2"}{"3+","3-","3"}{"4+","4-","4"}{"5+","5-","5"}{"6+","6-","6"}{"7+","7-","7"}{"8+","8-","8"}"9"; do echo "$i = $[i]"; done | grep " = 100$"

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Try doing that in MSDOS :D

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Attachment 68477

I blame Jacob Roman.

:lol:

1+2+3+4+5+6+7+8+9=45
1*2*3*4*5*6*7*8*9=362880

362880/45 = 8064

:eek2:

Quote:

---

Originally Posted by mudcake

1+2+3+4+5+6+7+8+9=45
1*2*3*4*5*6*7*8*9=362880

362880/45 = 8064

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:eek: A system of mathematical statements whose end result is of no significance to anything!

aka "Statistics"

*ba-dum-tish*