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A pair of dice is thrown and the score is obtained by finding the product of the two numbers on top of the dice when they land.
In five throws of both dice:

the second score is $5$ more that the first;
the third score is $6$ less than the scond;
the fourth score is $11$ more than the third;
the fifth score is $8$ less than the fourth.

What was the score for each of these five throws?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.