# When I was brushing my teeth

I came up with this puzzle in the morning when I was brushing my teeth.

3, 8, 4, 6, 5, 8, 6, 7, 7, 8, 8, ?

What should the next number be? Give your reasoning as well.

HINT:

Even number position represent letters

NOTE: I have edited my sequence, and the answer is not 8.

• is it important that you were brushing your teeth? or are you trying to tell us that good oral hygiene makes you better at creating puzzles? Aug 30, 2016 at 8:50
• @AmruthA no,it is not in OEIS. Aug 30, 2016 at 9:09
• Is this the order in which you brush your teeth by number? ;) Just kidding. Aug 30, 2016 at 9:18
• Tooth 8 was particularly dirty. ;-) Aug 30, 2016 at 20:48
• Are you sure its not 8. Looks like an 8 to me lol Aug 30, 2016 at 20:49

7

And the pattern is

3=Triangle
4=Square
5=Pentagon
6=Hexagon
7=Heptagon
8=Octagon

And

The even position numbers are the number of letters in the names of the regular polygons with those numbers of sides. Triangle has 7 letters, Square has 5, etc.

• What does "all contains equilateral triangle" mean? Sep 1, 2016 at 19:05
• It mean ....rhombus also contain four sides. Sep 1, 2016 at 19:06
• So you mean "Each one is a regular polygon"? Sep 1, 2016 at 19:07

7 ?

Because

As your hint says, every even number is a letter, giving 3H, 4F, 5H, 6G, 7H, 8?

Then

I thought, why don't I start drawing this on a chessboard, to see what this looks like.

It looks a bit like teeth, with the 4F representing the canine tooth (if you're a tiger, mine isn't that much bigger than my other teeth), and the last white (teeth are white) square that would follow is 8G, G being the 7th letter.

I'm not sure why your canine tooth would be black though unless you've just ripped into your prey (remember you're a tiger at this point) and the black is really red blood, or you've just eaten too many sugary sweets.

This kind of leaves a question as to

Why the chess references are backwards. Well, that's because you're looking in the mirror while brushing.

• Surely, the real question is how with my tiger paws am I able to play chess? Aug 31, 2016 at 9:20
• represents letters not letter. Aug 31, 2016 at 12:21
• It has nothing to do with my teeth. Aug 31, 2016 at 12:44

6

Because:

The second parts are letters, 3H, 4F, 5H, 6G, 7H, 8?

So:

To continue this patern, you'd have 8 to have an F, which is the equivalent of 6

• Sounds a better fit than my answer +1 Aug 31, 2016 at 9:22
• I don't understand why F is the next letter; could you make this clearer for those of us as stupid as I seem to be Aug 31, 2016 at 9:29
• Now that i'm thinking of it, it's not quite sure the patern is complete yet, so I guess it's just a hunch :S I guess since he said that it wasn't eight, it had couldn't go up, so my guess is that it should go down again, but could be seven too Aug 31, 2016 at 9:32
• @foitn I forgot he had said it can't be 8. Looks like I'll go back to mulling it over (and getting nowhere) again Aug 31, 2016 at 9:43
• Wrong answer! well try......i said letters not letter.(should be my second hint) Aug 31, 2016 at 12:17

9

Because (Let x = Other insignificant numbers)

3, x, 4, x, 5, x, 6, x, 7, x, 8, x, 9

• I feel so stupid. I will up vote as soon as I am able to. Aug 30, 2016 at 20:36
• Haha really? I thought no one was willing to give an answer because of how simple the puzzle was. But i think you may have made the puzzle more complex than what it actually was Aug 30, 2016 at 20:41
• This gives the second missing number. It doesn't answer the question. Aug 30, 2016 at 20:43
• Wrong answer.....it was a second missing number Aug 30, 2016 at 20:54
• Actually we have to find 12th number in the sequence, but @Tyler Johnson found 13th number..
– KSR
Aug 31, 2016 at 4:31