Post by Aaron Williams on Aug 23, 2007 21:17:42 GMT -5
Now that we've covered the basics, we can get into more advanced things!
Take the concept of single derivatives. If we have a number like 1019, and we want only one answer out of it, we have a number of options to explore.
First, one could simply add the numbers together ( 1+0+1+9 ). This, however, still yields a double digit ( 11 ). We'll save this for later as problem one.
Secondly, one might use multiplication. 1*0*1*9 = 0, so this will not work at this stage. Since multiplication does not work, we can assume that division will not work either.
Lastly, we have subtraction to consider. 1-0-1-9 = -9. Unless we know that the answer needed is a negative, we can assume that this will not work either. Of course in problem two and three there is always the possibility of more than one function being used in a single equation. However, as we learned previously, a coder will most likely only use multiple functions in a single equation if the intended code breaker knows the sequence of functions.
Now then, back to problem one. If we look into 11, it appears that we have arrived at a single path, as 1+1=2. HOWEVER, this is where a new technique comes in! While it is true that 2 is the only solution to be gained out of 11 (for 1 is a product of the equation), there is another way to derive a more likely answer. For this, let us look back for a second at the original equation...
Originally we had 1+1+0+9=11. HOWEVER, it is possable to section the equation while remaining within the bounds of the function rule. Lets try that now.
(1+1)=2 & (0+9)=9. Now then, we have two answers, 2 and 9. 2+9 = 11, if we follow the same path we did in the last paragraph. However, it is now possible to use a different function, as this is now a different equation. Multiplication would yield a multi-digit number, and division a fraction, so Subtraction is our most favorable option. Therefore we see that 9-2=7, and thus we have our advanced answer!
Take the concept of single derivatives. If we have a number like 1019, and we want only one answer out of it, we have a number of options to explore.
First, one could simply add the numbers together ( 1+0+1+9 ). This, however, still yields a double digit ( 11 ). We'll save this for later as problem one.
Secondly, one might use multiplication. 1*0*1*9 = 0, so this will not work at this stage. Since multiplication does not work, we can assume that division will not work either.
Lastly, we have subtraction to consider. 1-0-1-9 = -9. Unless we know that the answer needed is a negative, we can assume that this will not work either. Of course in problem two and three there is always the possibility of more than one function being used in a single equation. However, as we learned previously, a coder will most likely only use multiple functions in a single equation if the intended code breaker knows the sequence of functions.
Now then, back to problem one. If we look into 11, it appears that we have arrived at a single path, as 1+1=2. HOWEVER, this is where a new technique comes in! While it is true that 2 is the only solution to be gained out of 11 (for 1 is a product of the equation), there is another way to derive a more likely answer. For this, let us look back for a second at the original equation...
Originally we had 1+1+0+9=11. HOWEVER, it is possable to section the equation while remaining within the bounds of the function rule. Lets try that now.
(1+1)=2 & (0+9)=9. Now then, we have two answers, 2 and 9. 2+9 = 11, if we follow the same path we did in the last paragraph. However, it is now possible to use a different function, as this is now a different equation. Multiplication would yield a multi-digit number, and division a fraction, so Subtraction is our most favorable option. Therefore we see that 9-2=7, and thus we have our advanced answer!