A Puzzle - Algorithm Needed or Involved?

[wemack88]

I am trying to solve a puzzle. How do I find an algorithm (or a formula) behind a series of six two-digit numbers? (The numbers are as follows: 14, 21, 33, 41, 56, 68.) The two-digit numbers, although different from one another, are always the same ones given. Each time they are rearranged differently. I have been given 45 instances of these six two-digit numbers. I need to calculate the next sequence, the forty-sixth.

Is there a formula (an algorithm) to determine the answer?
Any help warmly received.

 

[neurocomp2003]

lots of algorithms you could attempt to use to solve this...
The two problems this puzzle might be that come to mind are
[0] the sequence maybe a permutation generator.
[1] something to do with modulus.

 

[Architeuthis Dux]

I understand the importance of finding patterns and using algorithms to solve problems. In this case, the given sequence of numbers may seem random, but there could be an underlying pattern or formula that can help us determine the next number in the sequence. To find this algorithm, we can use various methods such as mathematical analysis, pattern recognition, and trial and error.

One possible approach could be to plot the given numbers on a graph and see if there is a linear or non-linear trend. This can help us determine if there is a mathematical relationship between the numbers. Another method could be to look for patterns within the numbers themselves, such as the difference between each number or the sum of the digits.

Additionally, we could try using trial and error by testing different mathematical operations, such as addition, subtraction, multiplication, and division, on the given numbers to see if we can find a pattern.

It is also important to consider the context in which these numbers were given. Is there a specific theme or concept that could be related to the sequence? This could provide valuable insight into finding the algorithm.

In conclusion, while there is no guarantee that there is a formula or algorithm behind this sequence of numbers, using analytical thinking and various methods can help us uncover any underlying patterns or relationships. With enough exploration and experimentation, we may be able to determine the next number in the sequence and potentially even find the algorithm behind it.