The Code

Just in case you didn't know, BBC started recently a new TV series with the name "The Code". Apart from being a TV documentary, it is also a quest for the treasure hunt. Some of the questions, in this quest, are quite interesting. It's all about observing the patterns, nothing complicated.

For example, have a look at this puzzle. After about 20 minutes of looking at the pictures I came with the following solution:

For the "six-sided dice" the repeating numbers are 1,2,3. For the "eight-sided dice" the repeating numbers are 1,2,3,4. It looks like these numbers generate the others.

1. For the first "six-sided dice" - 1,2,3 generate 2,3,4
2 = 1 + 1¹
3 = 1 + 2¹
4 = 1 + 3¹

2. For the second "six-sided dice" - 1,2,3 generate 2,5,10
2 = 1 + 1²
5 = 1 + 2²
10 = 1 + 3²

3. For the third "six-sided dice" - 1,2,3 generate 2,9,28
2 = 1 + 1³
9 = 1 + 2³
28 = 1 + 3³

4. For the first "eight-sided dice" - 1,2,3,4 generate 2,3,4,5
2 = 1 + 1¹
3 = 1 + 2¹
4 = 1 + 3¹
5 = 1 + 4¹

5. For the second "eight-sided dice" - 1,2,3,4 generate 2,5,10,17
2 = 1 + 1²
5 = 1 + 2²
10 = 1 + 3²
17 = 1 + 4²

Now, following this pattern...

6. For the third "eight-sided dice" - 1,2,3,4 generate
1 + 1³ = 2
1 + 2³ = 9
1 + 3³ = 28
1 + 4³ = 65

And the answer is: 65