# Mathematical sequences challengeAugust 18, 2010 8:11 PM   Subscribe

Mathematical sequences challenge. Need your help.

I have these mathematical sequences that were given to me by my brother as a challenge. I believe they came from his daughter's homework, though we are not trying to help her cheat. He's just challenged me to solve them because he was unable. He wants to see how smart/resourceful I am. I'm allowed to use 'all the powers of the internet at my disposal' to try and solve these. (That's the resourceful part.) For me that includes you, I hope.

I think I may have the answers anyway, but I'd like your second opinion.

I've taken a picture of five of these sequences. The first two are simple and are solved. They are just there for example.

Pic

I believe that the soltion to the 3rd is:
1 , 1*2 , 1*2*3 , 24 , 1*2*3*4*5 , 1*2*3*4*5*6, 5040

The 4th and 5th I'm less confident about. I'm not sure what the subscripts mean. I guessed (perhaps incorrectly) that they represent a number system other than base 10. So base 5 and base 7. None of the numbers in the sequences so far violate those number systems. If that assumption is correct, I came up with the following:

1, 4, 12, 22, 23, 31 (with the little 5 subscripts)

and

1, 4, 12, 22, 34, 51, 100 (with the 7s)

I'm quite ready to believe that I'm wrong.

What do you think? Am I right? If not, what is?
posted by gummo to Education (7 answers total) 1 user marked this as a favorite

The third is a factorial.
posted by rancidchickn at 8:14 PM on August 18, 2010

This site is a very useful lookup tool for this sort of thing. (I've looked up your last sequence in the link).
posted by nat at 8:20 PM on August 18, 2010

Dude, all your happy little marks on the paper, I can't tell what's a negation, what's a multiplication, what's a subscript. Maybe you could actually type out the sequences?
posted by orthogonality at 8:22 PM on August 18, 2010

Yes, you're correct.

Yeah, three is factorial (1, 1x2, 1x2x3, 24 = 1x2x3x4).

Four is +3, expressed as numbers in base 5 (1, 4, 12, 20, all base 5 is 1, 4, 7, 10 in decimal, transform is +3). So the next 2 are 13, 16 in decimal, or 23, 31 in base 5.

Five is the first four perfect squares, in base 7 ( 1, 4, 12, 22, all base 7, is 1, 4, 9, 16 in decimal). So the next are 25, 36 in decimal, or 34, 51 in base 7.
posted by orthogonality at 8:32 PM on August 18, 2010 [2 favorites]

The third problem is numbers with dots between (multiplication?)

1, 1*2, 1*2*3, 24, ____ , ____

The 4th are just numbers with subscripts of 5. The numbers are:
1, 4, 12, 20, _____ , _____ , _____

The 5th are just numbers with subscripts of 7. The numbers are:
1, 4, 12, 22, ____ , ____ , ____
posted by gummo at 8:35 PM on August 18, 2010

I mistyped my proposed solution to the 4th item above. It should be:

1, 4, 12, 20, 23, 31, 34 (with little subscript 5s)
posted by gummo at 8:41 PM on August 18, 2010

The subscripts are probably bases; thats a pretty common standard.

1,4,12,20(base 5) is 1,4,7,10 in base 10, so next is 13 and 16 (base 10) which is 23 and 31 in base 5.

The next is similar but they go up by odd increments instead of a fixed value. I'll leave it up to you.
posted by chairface at 8:55 PM on August 18, 2010

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