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Topic: An interesting game (Read 620 times) |
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wonderful
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Posts: 203
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An interesting game
« on: Jun 12th, 2008, 11:13pm » |
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You are given two positive integers A and B. The object is to start with A and turn it into B, through a series of steps. In each step you can add, subtract, multiply by, divide by, or take the power/root of another positive integer.
Sound easy? There's another part: There is a COST for each modification, and you want to find the cheapest method to get from A to B. Let the number you are using = N.
Adding or subtracting N costs N dollars.
Multiplying or dividing by N costs N+2 dollars.
Powering or rooting with N costs 2N dollars. (You have 3 options here. If C is the current number, you can take C^N, N^C, or the Nth root of C.)
Your final total = the above costs + N dollars (where N is the number of steps in your method).
Remember-- Throughout your steps, the number must remain a positive integer. You can't subtract it to negative, or make it a fraction through division.
And lastly, you cannot multiply twice in a row or divide twice in a row.
So for example, try to get from 5 to 91.
1) Multiply by 18 (20 dollars)
2) Add 1 (1 dollar)
20 + 1 + 2 steps = 23.00
...or...
1) Add 2 (2 dollars)
2) Multiply by 13 (15 dollars)
2 + 15 + 2 steps = 19.00
How about:
12 to 345
64 to 729
6 to 8888
142857 to 100
Please feel free to aks more.
Have A Great Day!
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towr
wu::riddles Moderator
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Re: An interesting game
« Reply #1 on: Jun 13th, 2008, 2:06am » |
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12 to 345
((12-1)^2 -6)*3 20
64 to 729
((64^1/3) +1)^3 16
6 to 8888
((6^5)+1)/7*8 34
142857 to 100
(142857*7+1)^1/3 18 19
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| « Last Edit: Jun 13th, 2008, 11:29am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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rmsgrey
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Re: An interesting game
« Reply #2 on: Jun 13th, 2008, 9:34am » |
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I notice that the added cost of N for N steps is equivalent to increasing each step's price by 1, so:
+-N costs N+1
*/N costs N+3
power/root with N costs 2N+1
Also, alternate $19 routes for 5->91:
5*2=10 $5
10+3=13 $4
13*7=91 $10
or
5*3=15 $6
15-2=13 $3
13*7=91 $10
or
5+8=13 $9
13*7=91 $10
12 to 345
((12+1)^2+3)*2+1 $18
and I make the cost of towr's 142857 to 100 $19
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