Author |
Topic: Numbers (Read 626 times) |
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender: 
Posts: 4489
|
Each of ten boys sitting at a round table chooses a number and tells it to his neighbour on each side. Thus each child gives out one number and receives two. Each boy then reveals the average of the two numbers he received. Remarkably, in order round the table these numbers were 1,2,3,4,5,6,7,8,9,10.
What was the number chosen by the boy who revealed the number 6?
|
| « Last Edit: Oct 18th, 2008, 8:36am by ThudnBlunder » |
 IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
teekyman
Full Member
Gender:
Posts: 199
|
 |
Re: Numbers
« Reply #1 on: Oct 18th, 2008, 12:10pm » |
 Quote  Modify
|
1
|
|
IP Logged |
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: Numbers
« Reply #2 on: Oct 18th, 2008, 2:23pm » |
Quote Modify
|
on Oct 18th, 2008, 12:10pm, 1337b4k4 wrote:
I don't believe you. 
|
|
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
Gender:
Posts: 13730
|
|
Re: Numbers
« Reply #3 on: Oct 18th, 2008, 2:56pm » |
Quote Modify
|
on Oct 18th, 2008, 2:23pm, ThudanBlunder wrote:I don't believe you.
|
|
6, -3, -2, 9, 10, --> 1 <-- , 2, 13, 14, 5
By method of quickmath's advanced solve form, on 10 simultaneous equations
Because I'm too lazy to do it by hand
|
|
IP Logged |
Wikipedia, Google, Mathworld, Integer sequence DB
|
|
|
JohanC
Senior Riddler
Posts: 460
|
|
Re: Numbers
« Reply #4 on: Oct 18th, 2008, 2:59pm » |
Quote Modify
|
on Oct 18th, 2008, 2:23pm, ThudanBlunder wrote:
I don't believe you.
|
|
Why not?
Do you see another way to solve this other than just solve 2 systems of 5 straightforward linear equations?
|
|
IP Logged |
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Numbers
« Reply #5 on: Oct 18th, 2008, 3:18pm » |
Quote Modify
|
3 1
|
| « Last Edit: Oct 19th, 2008, 12:24am by Grimbal » |
IP Logged |
|
|
|
Hippo
Uberpuzzler
Gender:
Posts: 919
|
|
Re: Numbers
« Reply #6 on: Oct 18th, 2008, 5:26pm » |
Quote Modify
|
on Oct 18th, 2008, 2:59pm, JohanC wrote:
Why not?
Do you see another way to solve this other than just solve 2 systems of 5 straightforward linear equations? |
|
Of course you can see in it solving the 2 systems of 5 equations ... You can calculate the difference 4 steps around the circle as the difference of sums (twice average) involving them and another common value are known. Knowing the difference 4 steps around you can calculate the difference 8=(-2) steps around the circle. But knowing the difference and sum allows us to compute the number easily (and it differs form 3. The solution 1 is unique.)
|
| « Last Edit: Oct 18th, 2008, 5:28pm by Hippo » |
IP Logged |
|
|
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender:
Posts: 7527
|
|
Re: Numbers
« Reply #7 on: Oct 19th, 2008, 12:24am » |
Quote Modify
|
Hm... I checked my calculations and you'll be happy to hear that you are right now. 
|
|
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print