Question

Disks in a tower of Hanoi are identified from top to bottom as 1, 2, 3, and so on. A computer can solve the puzzle by listing each disk moved, in order. For example, a 3-disk puzzle is solved as 1-2-1-3-1-2-1. If it takes a computer 1 second to display the 10-disc solution, how long would it take to display the solution to a 30 disc tower?

Answer 1

thanks

Answer 2

Do you understand how this puzzle works?

Answer 3

i have played it before yes

Answer 4

What needs to be done in the puzzle?

Answer 5

ok so for a 3 disk puzzle, there are 3 hoops and 3 disks on the first hoop. The smallest disk is on the top, followed by a medium size and a large disk. in one move, you can only move one disk to another hoop of your choice. you cannot move a disk on top of a larger one. I can link u a small flash version of the game on mathisfun http://www.mathsisfun.com/games/towerofhanoi.html

Answer 6

Is there a formula for how many moves in a n-disc game?

Answer 7

i suppose this helped me http://mathworld.wolfram.com/TowerofHanoi.html

Answer 8

Is this from a class textbook or from a puzzle book?

Answer 9

the question is from class but the link is from a textbook explanation

Answer 10

i just can't decipher the textbook

Answer 11

waiiiiiiiiiiiit

Answer 12

this formula works

Answer 13

h\[h_{n} = 2^{n} -1\]

Answer 14

where h subscript n is total moves and n is the number of disks

Answer 15

Plug n = 10 into the formula and find the number of moves.
Plug n = 30 into the formula and find the number of moves.

Find the ratio.

The display time will be in the same ratio.

Answer 16

that will produce 1023 and 1073741823, whose ratio is 1049601 THANKS!

Answer 17

wait i have one last problem that is baffling me

Answer 18

Is 1049601 seconds the correct answer? Or do they want it in days, hours, minutes, seconds?

Answer 19

it doesnt matter i can solve it from this point

Answer 20

i just need help with one last

Answer 21

go ahead.

Answer 22

Determine a, b, and c if the number at the end of each row in the chart shown below is the sum of the numbers in the row. Find a rule that relates the numbers at the bottom of each column to the entries in the column.

Answer 23

sorry for bad drawing

Answer 24

1st row: b+c+a+c = a+b+2c = 54 --- (1)
2nd row: a+c+b+a = 2a+b+c = 50 --- (2)
3rd row: b+b+c+a = a+2b+c = 44 --- (3)

Three equations and three unknowns. Solve for a, b and c.

Answer 25

so a+b+c=37 which means a=13 b=7 c=17

Answer 26

is that the whole thing?
i dont understand the rule part

Answer 27

i mean, i understand it, im just having trouble locating the rule

Answer 28

Redraw the table with a,b,c filled in. Drop the last column (the row totals column) in the new table. We can take a look at it and see if some pattern pops up.