jurgen
Senior Heliman
Location: Weybridge, Surrey, UK
| I know the answer is already posted but seeing as I couldn't sleep I thought I'd share my improved logic to the answer.
(The first time I did it I used Excel to do it "Brute Force", now that I knew the answer I tried to 'reason' it out)
The list of possibles: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12and 13.
2 has to be in the list otherwise all the other even numbers would also have to be excluded because any number that is divisible by an even number is also divisible by 2.
4 has to be in the list otherwise 8 and 12 would have to be excluded as well. Same logic as above.
Because 2 and 4 are included we can include 3 (remember we are looking for 2 sequential numbers to exclude).
Now if 2 and 3 are included then the number we are looking for must be a multiple of 6 (so that 2 and 3 can divide into it, 6 is known as the LCM (lowest common multiple) of 2 and 3)
Because we have 4 and 6 we can include 5.
The LCM of 2, 3, 4, 5 and 6 = 60 so 10 and 12 also join the list as they can both divide into 60.
Because we have 10 and 12 in the list we can add 11 and 13 as well.
Already with only low numbers we almost have the whole list. The only numbers not in yet are 7, 8 and 9. So we know that 8 is one of the numbers that will be left out (because it has to be either 7, 8 or 8, 9).
This is where the numbers start to grow!  Stick with me!
LCM for 2, 3, 4, 5, 6, 10 and 12 is 60 (remember from above), so now I start adding one number at a time to that list.
LCM for 2, 3, 4, 5, 6, 10, 11 and 12 is 660 (60 X 11)
LCM for 2, 3, 4, 5, 6, 10, 11, 12 and 13 is 8580 (660 X 13)
8580 is not divisble by 7, 8 or 9 so we know we are still on the right track! Nearly there....
8580 X 2 = 17160 which is divisible by 8, no good.. 
8580 X 3 = 25740 which is divisible by 9 but not by 7 or 8! There's the answer!
rchelipilot121 do you have the working out of the original? Is there a better way to get to this answer? |
JEFF
