Puzzle

MrAl

Joined Jun 17, 2014
11,342
Hello,

With these problems that are not worked out that carefully there are often 'shortcuts".
I found a solution heuristic after looking at the problem for a few seconds, then tried it out using a calculator and apparently it worked. This is a very abstract way to handle these problems.

The heuristic goes as follows...
We are given:
1+4=5
2+5=12
3+6=21
8+11=?

We notice two things right away and then a third:
1. The solutions shown are not in pure math, therefore the numbers on the left are probably abstract representations of what is really there.
2. The solutions on the left increment by the same amount that the right sides increase by over the last increase. For example to get from 5 to 12 you have to add 7, and to get from 12 to 21 you have to add 9.
9 equals 7+2, and 3+6=2+5+2.
3. There seems to be a lot missing because the left 'column' of numbers goes 1,2,3 and then 8, so we are missing 4,5,6,7, and the second 'column' goes 4,5,6, 11, so we are missing 7,8,9,10. Thus there is also a one to one correspondence between the first two columns.

Finally, if we follow the same pattern it's just a matter of adding a number to the previous number where that number is 2 more than it was before. Thus we end with:
5+7=12
12+9=21
21+11=32
32+13=45
45+15=60
60+17=77
77+19=96

and you can see each successive row is just the last row total plus the last row addition term with two added to it. In data compression this would be similar to a differential encoding scheme were we encode the difference between the current quantity and the previous quantity instead of the whole absolute quantity itself, and we have just decoded a steam of data that happened to have a very smooth field.

You can try other methods too i guess.
 
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