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12-01-2016 , 05:26 PM
#126
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ok

something I clearly forgot to state:

you need to get to Miram Shah in 10 days
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12-01-2016 , 05:26 PM
#127
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Welp, you beat me to it.

Ignore me.
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12-01-2016 , 05:37 PM
#128
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Spoiler:
1093 helpers

You need help for 7 days. The answer is SUM[n=0 to 6](3^n)
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12-01-2016 , 05:38 PM
#129
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Bravo Lattimer
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12-01-2016 , 05:45 PM
#130
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Puzzle #8

You are in a store and it only sells 6 types of items:
Rubber Bands
Thumb Tacks
Pins
Paper Clips
Nails
Staples

Each item costs either 1¢, 2¢, 3¢, 4¢, 5¢ or 6¢ (repeats possible) and you don't know what anything costs.

If you buy a bunch of stuff then you are told the total cost but the receipt is not itemised.

You are allowed to make a single purchase and must be able to figure out the cost of each item. Your strategy must be as cost effective as possible.

What do you do?
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12-01-2016 , 05:56 PM
#131
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I wanna say

Spoiler:

Buy 1 of item A
7 of item B
7^2 of item C
7^3 of item D
7^4 of item E
7^5 of item F

But there might be a cheaper way?
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12-01-2016 , 05:57 PM
#132
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Quote:
Originally Posted by iraisetoomuch
I wanna say

Spoiler:

Buy 1 of item A
7 of item B
7^2 of item C
7^3 of item D
7^4 of item E
7^5 of item F

But there might be a cheaper way?
tell me more...
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12-01-2016 , 06:01 PM
#133
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Quote:
Originally Posted by iraisetoomuch
I wanna say

Spoiler:

Buy 1 of item A
7 of item B
7^2 of item C
7^3 of item D
7^4 of item E
7^5 of item F

But there might be a cheaper way?
Correct! Nice. Work shown in spoiler...

Spoiler:
Think of it in terms of a base 7 numbering system...
Total cost of item A will be either 1, 2, 3...6
Total cost of item B will be either 10, 20, 30...60
Total cost of item C will be either 100, 200, 300...600
etc...
So when you convert the total cost to base 7, you can easily determine each item's cost.
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12-01-2016 , 06:05 PM
#134
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^
Yup.
That.
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12-01-2016 , 06:43 PM
#135
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Spoiler:
you only need to do

1,6,6^2,...

since it's a base 6 number system

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12-01-2016 , 06:49 PM
#136
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Base 6 only has the digits 0, 1, 2, 3, 4 & 5

If something costs 6 cents then it now costs 10 cents and will affect the next item
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12-01-2016 , 06:55 PM
#137
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Spoiler:

it doesn't matter. each set of prices will produce a unique total

e.g. for two items, with possible prices of 1c or 2c, buy 1 of item A and 2 of item B,

A=1c, B=1c -> 3c
A=2c, B=1c -> 4c
A=1c, B=2c -> 5c
A=2c, B=2c -> 6c

you can do it out in a spreadsheet for 3 items, 4 items, etc and see that it works
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12-01-2016 , 07:01 PM
#138
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DM is right, each combination will produce a unique sum. I made the mistake of just padding the front of the number line - that still works, but it's not optimal.
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12-01-2016 , 07:03 PM
#139
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Is there any way of looking at the cost and figuring out the cost of everything other than looking up the cost in the spreadsheet?
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12-01-2016 , 07:13 PM
#140
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Spoiler:
1. Subtract total cost by 1, then divide by 6. The remainder + 1 is Item A cost.
2. Subtract above quotient by 1, then divide by 6. The remainder + 1 is Item B cost.
3. Subtract above quotient by 1, then divide by 6. The remainder + 1 is Item C cost.
etc...

If the possible prices were 2-7 instead of 1-6, you would do the same above, but add/subtract by 2 instead. Basically, if the prices are sequential, the step is: Subtract by (min range value), divide by (number of items), remainder + (min range value) is the cost for that item. Lather rinse repeat.
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12-02-2016 , 02:53 AM
#141
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Puzzle #9:

There are 50 wires running under the Hudson river with ends for each wire sticking out on both the east and west bank. All wires look the same and you can't tell which end matches up with which. The only way you have to tell which is which is to connect wires at see if they form a circuit. How many trips across the Hudson is required before you can tell exactly which wire is which?
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12-02-2016 , 11:03 AM
#142
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This was a fun one.

Answer:

Spoiler:
2


Explanation:

Spoiler:

Connect the first 9 wires together, then the next 8 together, etc. down to 2. Call them groups A through H. There will be 6 wires left over, keep them unconnected. Call them group I.

Go to the other side of the river.

I'll hide the second part of the answer in case anyone wants to figure the rest out themselves..

Spoiler:
By testing wires together you can determine which are connected to 8 others (group A), 7 others (group B), etc. Wires not connected to any belong to group I.

From groups A-H, take the first wire from each and connect them together, call this group J. Then connect the second wire from groups A-G (leave the second from group H unconnected), call this group K. Connect the third wires from groups A-F, the fourth wires from groups A-E, etc. Then connect all of the group I wires to different groups (doesn't matter which).

Cross back to the original side of the river.

Now you can test wires to determine which from each of groups A-I belong to each of the groups created on the other side of the river, identifying every connection.
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12-02-2016 , 11:30 AM
#143
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Nice, I came up with a way that was similar but it required 1 more trip.
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12-02-2016 , 05:37 PM
#144
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Good work DM
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12-02-2016 , 05:41 PM
#145
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Puzzle #10

Two robots are parachuted onto a number line. They land randomly on an integer and their parachute detaches. You have to program them so that they meet. You have to give both robots identical programming and you are restricted to the following options:

-Move left 1
-Move right 1
-Go to line of programming __
-If standing on a parachute then move right 1
-If standing on a parachute then move left 1
-If standing on a parachute then go to line of programming __

What is your program?
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12-02-2016 , 07:22 PM
#146
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Parachute detaches on the spot they land?
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12-02-2016 , 07:46 PM
#147
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Do they have to start in the same spot in the identical programming?
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12-02-2016 , 07:50 PM
#148
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Spoiler:
Move right 1
If on parachute go to line 4
Go to line 1
If on parachute move right 1
Move left 1
Go to line 4
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12-02-2016 , 08:52 PM
#149
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Quote:
Originally Posted by chuckleslovakian
Spoiler:
Move right 1
If on parachute go to line 4
Go to line 1
If on parachute move right 1
Move left 1
Go to line 4
Very close!
Spoiler:
Have the robot take 1 left then 2 right until it reaches the other parachute. After that just keep going right.
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12-03-2016 , 04:33 AM
#150
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Quote:
Originally Posted by housenuts
Parachute detaches on the spot they land?
yes

Quote:
Originally Posted by iraisetoomuch
Do they have to start in the same spot in the identical programming?
yes
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