74 replies to this topic

[Gleeok]

You can notate it by n!, or "n factorial."

Yep. That is indeed what I was looking for.

1, 4, 7, 11, 14, 17, 41, 44, 47, ___

71

(Let's try another slightly different one)

1, 10, 1001, 10010110, 1001011001101001, ?

[Lightwulf]

Translating from binary, it's: 1, 2, 9, 150, 38505, ?

However, I couldn't figure out a sequence with those. So this is what I came up with: 10010110011010010110100110010110

Calculation:

Each successive term takes the inverse of the previous entry, and then tacks the previous term in front of the inverse of it.

The inverse of 1 is 0; the second term puts the previous term (1) in front of the inverse of that tern (0) to make "10".
Likewise, the third term puts the previous term (10) in front of the inverse of that term (01) to make "1001".
That's how I got it!

That one really made me think. Nice one, Gleeok!

Here's the next one from me:

256, 64, 112, 28, 49, 12.25, ___

[nicklegends]

The sequence alternates between dividing the previous term by 4 and multiplying it by 7/4. The next term is 12.25*1.75 = 21.4375.

Next sequence...

2, 4, 8, 61, 221, 244, 884, 8671, ___

This one could be tricky, so I'll offer a hint.

Hint

Multiply the previous term by two, then manipulate the answer.

[Lightwulf]

The sequence alternates between dividing the previous term by 4 and multiplying it by 7/4. The next term is 12.25*1.75 = 21.4375.

Well, you got the answer right even though it wasn't the same method I used; I was alternating between subtracting 75% and adding 75% from the previous term, but essentially it's the same thing as what you did. Your method probably had less math steps than mine.

Anyway, about your sequence, thanks for the hint; I'm not sure if I would've figured it out otherwise.
You took 2 times the previous term and then reversed the number order, making 16 into 61. So, the final answer is 24371.

Next sequence:

16, 8, 4, 2, 6, 18, 54, 162, 40.5, __

[nicklegends]

Well, let's see. We start off dividing the terms by 2, then we multiply them by 3, then we begin dividing by 4 at the end. I suspect the answer is 40.5/4 = 10.125.

3, 27, 19683, 7625597484987, ___

[nicklegends]

Hmmm. I guess that one is a little tough because it isn't a calculation you can really do in your head. The answer is to cube the previous number. Thus, the answer is 443426488243037769948249630619149892803, or in English, four hundred forty-three undecillion four hundred twenty-six decillion four hundred eighty-eight nonillion two hundred forty-three octillion thirty-seven septillion seven hundred sixty-nine sextillion nine hundred forty-eight quintillion two hundred forty-nine quadrillion six hundred thirty trillion six hundred nineteen billion one hundred forty-nine million eight hundred ninety-two thousand eight hundred three. It's a big number. Anyway, try this one next.

1, 221, 333221, 4444333221, ___

[XMSB]

555554444333221, the quantity of each digit is equal to the digit itself.

1, 5, 9, 15, __

[nicklegends]

There aren't enough terms to really know for sure, but I'll guess that the answer is 25. Each term seems to be the square of its index, with a +0, +1, +0, -1, pattern going. Therefore, the next term would seem to be 25+0 = 25. You probably had something else in mind, though...

Anyway, here's a good one for board game players.

1, 3, 3, 2, 1, 4, 2, 4, 1, ___

Hint

The sequence corresponds to A, B, C, D, E, F, G, H, I, and J in order.

Hint 2

There are two pieces of info on each Scrabble tile.

[XMSB]

8, because that's how many points the J tile is worth.

There aren't enough terms to really know for sure, but I'll guess that the answer is 25. Each term seems to be the square of its index, with a +0, +1, +0, -1, pattern going. Therefore, the next term would seem to be 25+0 = 25. You probably had something else in mind, though...

I'm sorry, the correct answer is 21, because the numbers in my pattern correspond to the vowels in the alphabet, and what order they appear in. A is the 1st letter, E is the 5th, I is the 9th, O is the 15, and U is the 21st.

Anyway...

10, 1, 1, 1, _

(Hint: Taking another page from Scrabble, the word this pattern corresponds to is quilt)

[nicklegends]

The answer is 1 because a T is worth one point. (For comparison, the Q is 10, the U is 1, the I is 1, and the L is 1.)

100, 72, 93, 78, 86, 84, 79, 90, 72, ___

[Lightwulf]

The answer is 96.
The pattern is alternating between adding and subtracting a number, starting at 28, which value is decreased by 7 and 6, alternating per term. (The first number is subtracted by +28; 2nd - adding +21 (28-7); 3rd - subtracting +15 (21-6); 4th - adding +8 (15-7); 5th - subtracting +2 (8-6); 6th - adding -5 (2-7); 7th - subtracting -11 (-5-6), meaning adding 11; 8th - adding -18 (-11-7), meaning subtracting 18; and 9th - subtracting -24 (-18-6), meaning adding 24. So, 72+24=96.
Nice one!

Here's the next one:

1, 2, 6, 2.5, 12.5, 75, 10.714, ___

[nicklegends]

I think the pattern is to multiply, multiply, then divide ascending consecutive integers, but if that's true, then you made a mistake in saying 6/4 is 2.5, since it should be 1.5...

1
1*2 = 2
2*3 = 6
6/4 = 2.5**
2.5*5 = 12.5
12.5*6 = 75
75/7 = 10.714
10.714*8 = 85.714


Try this one next...
1, 2, 3, 3, 4, 5, 4, 5, 6, 7, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 11, ___

Hint me, bro

Look at the first digit, then the next two, then the next three, etc.

[JetBox]

I get it. Whatever number it is on, it counts up that many times, so 7.


okay, 1-7-21-46-85-141-?

I kind of came in randomly here, so ya.

[nicklegends]

I couldn't figure that one out. I'll start a new one, but feel free to explain the trick.

3, 8, 24, 48, 120, 168, ___

Hint

Try adding one to each term above and see if the numbers become any more recognizable.

[Mero]

17 squared - 1

4.5
4.1
4.3
4
4.1
3.6
4
3.2
3.6
____

Edited by blackbishop89, 23 December 2012 - 07:14 PM.