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#342171 Splitting the pizza costs fairly
Posted by DeGe on 02 June 2015  12:54 PM
#342076 Arms across the world
Posted by DeGe on 24 April 2015  01:29 PM
The average is <2 arms
 1
#340512 Please be obtuse!
Posted by DeGe on 07 October 2014  10:29 AM
Choose any 2 points shown with the blue line below;
Now, as long as the third point is within the two red lines, the triangle is acute otherwise obtuse
For an infinte plance, the probability of third point within these two lines is near zero.
 1
#339805 Weighing machines
Posted by DeGe on 25 August 2014  02:04 PM
Ah the editor did not let me change the formatting while editing.
In the previous post, I copy pasted from excel. While editing it showed things fine but the final result was all messed up as you can see in the previous post.
This should look better
I would recommend to use the digital scale.
In max 5 weighings, the swapped pair of eggs can be identified:
Weigh 1 to 6 number eggs It should weigh 15
If it weighs other than 15, refer to weighings A below  max 2 more weighings needed
If weight > by Possible egg switches
1 6 & 7
2 6 & 8 5 & 7
3 6 &9 5 & 8 4 & 7
4 6 & 10 5 & 9 4 & 8 3 & 7
5 6 & 11 5 & 10 4 & 9 3 & 8 2 & 7
6 6 & 12 5 & 11 4 & 10 3 & 9 2 & 8
7 5 & 12 4 & 11 3 & 10 2 & 9 1 & 8
8 4 & 12 3 & 11 2 & 10 1 & 9
Taking worst case example where there are 5 possibilities
Weigh 6 10 4 8
If weight is +5, possibilities are 6 &11, 4 &9
If weight is 5, then possibilities are 5 &10, 3 &8
If there is no difference then eggs 2 &7 are swapped
Depending on the weight difference, whoose either 6&9 or 5&8 to weigh
Depending on the next weigh difference (+5 or 5), the swapped eggs are identified
Otherwise Weigh 2 4 6 8 10 12
It should weigh 42
If it weighs other than 42, refer to weighings "B" below  max 3 more weighings needed
If weight difference Possible egg switches
5 1 6 7 12
3 1 4 6 3 10 7 12 9
1 1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 8 9 10 11
3 2 5 8 11
Next, Weigh alternate weights from the weight difference
Taking worst case example where there are 6 possibilties (1 weigh difference)  weigh 1 4 5 8
Possbilities Possible egg switches
+1 1 2 5 6
1 3 4 7 8
0 9 10 11 12
Now, If weight difference Weigh
+1 1 & 6
1 3 & 8
0 9 & 12
A positive or negative weight difference in this weighing identifies the swapped pair
For example if in weighing 1&6, the weight is 6, then the swapped eggs are 5 &6
If the weight is 8, then swapped eggs are 1 & 2
Otherwise Weigh 1 2 11 12
It should weigh 26
If it weighs other than 42, refer to weighings "C" below
Weight Difference Possible egg switches
4 1 5 2 6
2 1 3 2 4
2 10 12 9 11
4 8 12 7 11
0 4 6 3 5 8 10 7 9
For the two possible pairs weigh any one egg out of the 4. If the weight is ok, the other pair is swapped. If the weight is not ok, you have identified the swapped pair
Otherwise Weigh 3 4 10 It should weigh 17 If it weighs 17, then eggs 7 &9 are swapped If it weighs (2) 15, then eggs 8 & 10 are swapped Otherwise, it weighs 19 (+2) and the possibilites are 3&5 or 4&6 are swapped Weigh 3 If it weighs 5, then eggs 3 & 5 are swapped Otherwise eggs 4 & 6 are swapped
[/spoiler]
 1
#338713 Two interesting puzzles (1 easy, 1 unsolved)
Posted by DeGe on 24 June 2014  09:37 AM
For the second, is there a picture you wanted to upload that did not get uploaded or is "vwQRZ1Y.png" the clue?
 1
#338688 Four numbers equals two dozen
Posted by DeGe on 22 June 2014  03:49 PM
Thanx everyone for an interesting debate.
I wish real life were also as clear as pcia wants the op to be. I won't check it again, perhaps.
 0
#336151 A Prisoner Problem
Posted by DeGe on 11 October 2013  03:07 PM
Also they decide that any prisoner (except first) going to the room will toggle the switch on IF it is off otherwise will not toggle the switch. And, any prisoner (except first) will toggle the switch ONLY once.
The first prisoner will always toggle the switch off and count the number of times he does so. When he has a count of 99 toggles to off (other than his own on the first day if the bulb wasn't off) , he announces the passage of all 100 prisoners.
 1
#334798 Chaos calculation
Posted by DeGe on 29 July 2013  12:28 PM
Spoiler for TriangleBy brute force, 3/4 of the space is white
Now, I need to get the creativity points
The white area is 100%!
I think this result is mainly because we are considering area (in black) covered by points; which by definition have an area of 0.
 1
#334686 Up
Posted by DeGe on 24 July 2013  09:13 PM
The balloon with bag number 3 is not involved in any exchange. The ballons with 5 and 1 lb bags exchange once and the ballons with 4 and 2 lbs bags exchange once.
Total time taken is 1000/3 = 333.3 secs; Both 4/2 and5/1 exchange the bags at exactly 166.67 secs.
 1
#334121 double game
Posted by DeGe on 12 July 2013  01:00 PM
J 10
L 66
S 34
 1
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