P7

newsgroups: braincell.hot received: from mailqueue by vayu (mercury 1.21); 21 mar 100 21:24:52 ist+530 from: "d.suresh kumar" <[email protected]> organization: r.e.c., tiruchirappalli, india to: braincell.hot%[email protected] date: tue, 21 mar 2000 21:24:36 ist+530 subject: round #7 priority: normal x-mailer: pegasus mail v3.40 dear friends, here is the 7 th round of puzzles........ all the best.......... 1. there are 'n' lines in a plane, none of the two are parallel and no three of which pass through the same point. all the points of intersection are joined. how many new lines ( i.e. excluding the already existing lines) are formed by doing so? 2. there are 100 bulbs numbered from 1 to 100 all of which are initially off. the 1st bulb is on and all its multiples are switched on. 2nd bulb and all its multiples are toggled(i.e. 4,6,... are switched on if they are off and off if they are on). then 3rd bulb and its multiples are toggled.this procedure is carried out for all the bulbs. at the end which of the bulbs will be on? 3. find a point in an equilateral triangle such that if perpendiculars are dropped from this point, the sum of their lengths should be minimum. (thank you raykar for this contribution....) all the best............... contact me for further clarification, if required........ suresh.