<t>Had a late night thought (which can be disastrous) but here goes. Consider the orthogonal vectors v1=(1/n,1/n,1/n ... 1/n), v2=(1, -1, 0, 0, 0 ..), (1, 1, -2, 0 , 0 ,0 ...), (1,1,1, -3, 0,0,0 ..) ..... vn=(1, 1, 1, 1 .... -n-1). x1 + x2 ... +xn = 1 is satisifed by x=v1 + l2v2+l3v3 ... +lnvn for a...

How about n uniform U(0,c) ... add them up ... rescale so total is 1 and redo process if any of them is now greater than c.

<t>Think this works. Give each colour a number from 0 to n-1. If we add up all the colours in the room then the answer mod n must be one of 0,1, ... n-1. Person 1 presumes that the total mod n is 0 and works out what his colour needs to be to get that total. Similarly Person 2 works with a total of ...

If no option then either (1,2,3,4,5,6) av 3.5If option then if 1,2,3 I will have another go so (3.5,3.5,3.5,4,5,6) av 4.254.25-3.5 = 0.75Mike

<t>"Example : Student A thinks of the number 3 and Student B thinks of the number 4 ...on board the Teacher writes 7 and 8 . So Student A thinks B has either thought 4 or 5 which one he doesn't know so he says "NO"."Not sure I understand the question. If the teacher writes 7 & 8 then A knows tha...

The solution has to be symmetric in abc - so I think it is the minimum of the 3 alternative expressions

<t>Suppose that when I look around I see one white dot and everyone else has black dots. After 1 minute (say, choose your own value), the one (A) with the white dot dies. How can I distinguish between "A has just realised that everyone else has a black spot" and "A has already concluded that I would...