Look at the sequence
Here's a little hint:
"A little Hexa-Flexa
Don't let it vex ya."
1 , 64 , 729 , 4096 , 15625 , 46656 , __?__
P.S. I didn't use the hint. If you need a different hint, let me know.
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16 comments:
This puzzle makes no sense to me. None of the numbers are related to each other.
There is a relationship. You need to break down each number to find how they are related. Think about what you learned in sixth grade.
can we see the other hint? I don't get this at all
Ok I was on a roll with this but then came to a stop.. So far I figured this out:
1*64=64 (there are 0 numbers between them in the patern)
64*64=4096 (1 number between them)
729*64=46656 (3 numbers between them
4096*64=262144<-- which is now found to be the number after the first missing number. (4 numbers between them)
and so on... But I had to stop at the missing number, since I didn't know what to multiply by 64.
Grr... any other hints Mrs. Burke? :] The first hint lead me to researching hex on the coputer and I found hexdecimal which is in base 16... does this have anything to do with the pattern?
By the way, does everything I just said make any sense?
Oh and another connection(I think?) Hex=6, like a hexagon. After doing my little pattern, I found out that the missing number would have six numbers between it and it multiplied by 64.
Feel better Mrs. Burke!
Is it a conincidence that every other number is divisable by 16? Cause if not the next number will not be
okay i just found out hexa is another name for base 16 so it def has something to do with that
I figured out that every other number is divisible by eight, starting with 64, or the last three numbers are .125. Therefore, since 46656 is divisible by eight, the next number must end in .125. That's all I have gotten so far. Does this make sense to people?
I think I figured it out! Sarah thanks for the info about base 16. What I did was divided the last four numbers in the puzzle by 16. Then I noticed that 4096/16 is a perfect square. So I then found the square root of every number. Here is what I found (original number-number divided by 16-square root.): 729-45.5625-6.75, 4096-256-16, 15625-976.5625-31.25, 46656-2916-54. I then looked at the square roots and did 54/6.75 and got 8. In the sequence, those numbers are 3 apart. 4096 and the blank number are also 3 apart. I then did 16*8 to find the square root of the blank number/16. It was 128. Then I squared that to get 16384. Then i multiplied that by 16 to get the blank number and got 262144. Is this correct? I know it does sound extremely confusing.
Holy Camole! I think we should talk about this next math class.
Good job, Tommy!
The next number in the sequence is 117,649. When the problem said hexa I thought six sides. Then I realized, 1*1*1*1*1*1=1, 2*2*2*2*2*2=64, 3*3*3*3*3*3=729, 4*4*4*4*4*4=4069, and so on for all the other numbers. For the next number in the sequence I multiplied 7*7*7*7*7*7=117,649.
Oh and also, thanks for the hint Mrs. Burke. When you said break the numbers down and sixth grade it made me think prime factorization which lead me to get the first two numbers in the sequence.
Wow you guys are good. But tommy i think you found the second missing number and gofigure gound the first
Yeah cbcgaga is actually right, because based on my pattern thingy, 262144 would be the second missing number. Anyway, good job everyone for figuring it out!
THe first time i looked at this, I thought the pattern had to do with numbers times eight(because of 64). I thought it was numbers*8^2(1*8^2= 64, 64*8^2=4096 729*8^2=46656). Going by this pattern the missing number would be 1000000 (15625*8^2). Then I realized that this wouldn't work because 4096*8^2=262144(not a number in the pattern). I saw the hint about then and started looking for relationships with six in them. I got the relationship once I started thinking about powers of ten again. 1^6 = 1, 2^6 = 64, 3^6 = 729, 4^6 = 4096, 5^6 = 15265, and 6^6 = 46656. The missing number will be 7^6, which equals 117649.
I am so glad that Go Figure remembered prime factorization. I initially looked at the sequence as the cubes of the squares of numbers, i.e. 1 squared then cubed, 2 squared then cubed (4 cubed), 3 squared then cubed (9 cubed), etc. Did anyone think that way?
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