I think I solved the problem backwards but I ended up with the same answer. I made a table of what I know vs what my friend knows. I know they have 6 or 8. If

I think I solved the problem backwards but I ended up with the same answer. I made a table of what I know vs what my friend knows. I know they have 6 or 8. If they have 6, then I have 12 or 14. If they have 8, then I have 10 or 12. | Me Them || Them Me | Them Me | -------------------------------------------------------------------------------------------- I have | 12 6 .. 8 || 6 12 .. 14 | 8 10 .. 12 | They have | 6, 8 12 14..10 12 || 12,14 6 8 .. 4 6 | 10,12 8 10 .. 6 8 | The first column is what I see and what I know about my friend. The 2nd and 3rd columns are what this table looks like to my friend. ----------- My friend has 6 or 8. 4 is the first number to appear on the table so start on day 4. Day 4: If my friend has 6, he thinks I have 12 or 14. If I have 14, then I would have notified the caretaker today because now 14 + 6 = 20. Now he knows I don't have 14. As a result, if he has 6 then he knows I have 12 and should tell the caretaker that the total number is 18. | Me Them || Them Me | Them Me | -------------------------------------------------------------------------------------------- I have | 12 6 .. 8 || 6 12 .. | 8 10 .. 12 | They have | 6, 8 12 ..10 12 || 12 6 8 .. | 10,12 8 10 .. 6 8 | Day 5: I don't have 14, and now my friend knows that. If he has 6, he should now have alerted the caretaker the number is 18. He did not. This means he does not 6. | Me Them || Them Me | Them Me | -------------------------------------------------------------------------------------------- I have | 12 .. 8 || | 8 10 .. 12 | They have | 8 ..10 12 || | 10,12 8 10 .. 6 8 | So Day 5 I know I have 12 and he has 8.