Olympiad Question

closed account (13bSLyTq)
Hi,

Recently I have tried to do few Olympiad problems to get my logic up to speed however whilst doing a question, I was left confused with the question. To elaborate, please look at question 2: Die Tipping on 2010 British Olympiad Paper: http://www.olympiad.org.uk/papers/2010/bio/bio-10-exam.pdf

Now, I understand the concept of what it asks me to do however in page 4 of the paper it shows a sample input and output so firstly I understand the first input:


1 3 5
1 6 5
1 1 5


I understand that it is taking in the 3x3 board however the output after the next move confused me very much:


1 1 1
1 3 5
1 1 5



I don't see how that could be possible as firstly the die will start at coordinate (1,0) (i.e the part of the grid-inputted which was 3) and since the die is in its default orientation (1 facing up and 6 facing down) when next move happens surely the board should be:


1 4 1
1 2 5
1 1 5


Could someone explain what is wrong in my logic or at least write a re-mastered version of the question which is more clear?

Kind Regards,
OrionMaster
Last edited on
The die begins in the centre of the grid, that is where the 6 is.

1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 3 5 1 1 1 1
1 1 1 1 1 6 5 1 1 1 1
1 1 1 1 1 1 5 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1


current square number + uppermost die number = 6 + 1 = 7
The result is greater than 6 so we need to subtract: 7 - 6 = 1

This means the 6 should be replaced with 1.

1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 3 5 1 1 1 1
1 1 1 1 1 1 5 1 1 1 1
1 1 1 1 1 1 5 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1

The rule for 1 says the die should move in the direction of the heading (up), so the new location of the die will be where the 3 is.

1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 3 5 1 1 1 1
1 1 1 1 1 1 5 1 1 1 1
1 1 1 1 1 1 5 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
Last edited on
closed account (13bSLyTq)
@Peter87

That drawing out was amazing thank you for helping me actually understand this damn problem!

Thanks once again.
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