# 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? – Marius Aug 30 '16 at 8:50
• @AmruthA no,it is not in OEIS. – Numberknot Aug 30 '16 at 9:09
• Is this the order in which you brush your teeth by number? ;) Just kidding. – rhsquared Aug 30 '16 at 9:18
• Tooth 8 was particularly dirty. ;-) – celtschk Aug 30 '16 at 20:48
• Are you sure its not 8. Looks like an 8 to me lol – Avik Mohan Aug 30 '16 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? – Dan Russell Sep 1 '16 at 19:05
• It mean ....rhombus also contain four sides. – Numberknot Sep 1 '16 at 19:06
• So you mean "Each one is a regular polygon"? – Dan Russell Sep 1 '16 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? – Teddysted Aug 31 '16 at 9:20
• represents letters not letter. – Numberknot Aug 31 '16 at 12:21
• It has nothing to do with my teeth. – Numberknot Aug 31 '16 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 – bg6471 Aug 31 '16 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 – Teddysted Aug 31 '16 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 – Foitn Aug 31 '16 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 – Teddysted Aug 31 '16 at 9:43
• Wrong answer! well try......i said letters not letter.(should be my second hint) – Numberknot Aug 31 '16 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. – Teddysted Aug 30 '16 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 – bill bsl Aug 30 '16 at 20:41
• This gives the second missing number. It doesn't answer the question. – Avik Mohan Aug 30 '16 at 20:43
• Wrong answer.....it was a second missing number – Numberknot Aug 30 '16 at 20:54
• Actually we have to find 12th number in the sequence, but @Tyler Johnson found 13th number.. – KSR Aug 31 '16 at 4:31