Hi, Chris

Darryl is away on holidays so I am using his posting to chat with you. Apparently and according to Darryl that is not the approach the teach gave. He said something like divide into parts, well I don't think he knows what I am talking or rather I did not catch what he means. I will find out and perhaps, if you are interested, I will let you know.

What do you mean when you wrote, I quote,"Really coincidental and lucky for us." I am curious to know the reason and if he had done something good to the Onsponge community than I am glad, at least he has contributed.

Yes I would be interested to understand how the teacher solved the question. It's always good to see other approaches

For your question ... I just meant that we are fortunate that Observer posted the same question on his/her blog site around the same time otherwise Perseverance may have not noticed that solution to be able to share with us.

Hi, Chris

Okay, I will post the teacher's solution once I got it from Darryl.

Oic, in other words, there were 2 posts of the same question, 1 from Darryl and the other from an Observer's blog around the same time. That is indeed a timely coincident.

Hi, Chris

I managed to locate Darryl's maths paper and found the teacher's solution to the question. As I have guessed earlier, it is the Guess and check method.

May I ask you for a favour to tell where I can find information on how to determine the position of a number, letter, shape or something within a pattern like A B C D D C B A A B C D D C B A ................? 79th.

Thank You

May I ask you for a favour to tell where I can find information on how to determine the position of a number, letter, shape or something within a pattern like A B C D D C B A A B C D D C B A ................? 79th.

I'm not sure you will find something that works in all situations. In fact that would be rather difficult as each Pattern could be different. Therefore, at most, I think you will find a general statement which says: Solve the Pattern first. Find the position, trying small examples if necessary, establish the position. I know very vague. Let's take your example

A B C D D C B A A B C D D C B A

When I read this I see an immediate pattern which could be highlighted by changing the letters to numbers ...
A B C D D C B A A B C D D C B A (Original)
1 2 3 4 4 3 2 1 1 2 3 4 4 3 2 1 (Converted to numbers)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 (Position)

So we see the numbers grow to 4 (1,2,3,4) and then reverse (4,3,2,1). Further more, the position at the end of each increasing sequence is an odd multiple of 4 (1x4, 3x4, 5x4, ...) whereas the end of each decrease is an even multiple of 4 (2x4, 4x4, 6x4, ...). The 79th position is 1 less than an even multiple of 4 (80) therefore, in the 79th position will be the number 2 which is always the letter B.

Hi, Chris,

Thank you for your reply. I know there is such thing as " one-fit-all" solution in solving pattern.

The example I gave is easy to solve, but when you come to question like

AMIRAMIRAMIR...

where you are given the 12 letters in the patten and is asked to determine what the 2008th letter is, can be somewhat harder because of its 4 digits position.

I was hoping that there are articles written on this subject of pattens to enable me to read them and be better informed.....

Thank you again and have a good day.

Hi again,

There might be some books related to this, I cannot think of any off hand - perhaps that is a hint to create a new one

I would do this question the same way. In fact, most of these patterns I turn into numbers to see if I can see a pattern from the start. This does not always work however, more often then not it does help in my opinion.

AMIRAMIRAMIR
123412341234

Since 2008 is divisible by 4, then I know that the 2008 position will be 4. Therefore, there is an R in the 2008th position. If they asked for the 2006th position then I just subtract 2 positions and would get a 2 or the 'M'.

I think I did it before.

Hi, Chris


Thank you. And going back to the earlier question involving reversing pattern, would it be correct to say that the letter in the 69th position is the letter D?

Yes exactly. The 69th position is 1 more than an odd multiple of 4. Therefore the number 4 and the letter D. Well done.