I will give 4 dollars and ask the waiter to keep the change

Make four groups of 3 piles and last 1 pile is kept away for while .now take 1 coin from every pile of 1 st group and 2 coins from every pile of 2 Nd group ……so on and put on the scale .

Expected weight is 30x divide the reading on the machine by 30 if the remainder is (25,30) or dividing by 30 remainder is (0,5) you get x in each case and now put back in original form then from different associated in 4th group take 1 from 1 pile and 3 from 1 and 4 from 1.

Similarly, from 3rd group take 1 coin from 1 pile and 2 coins from another and 4 from another .now from 1 St group 2 coin from 1 pile and 3 coins from another and 4 th from another from 2nd group take1 coin from 1 pile take 3 from another and 0 from 1 pile now put on the scale if no error then the pile 0 are chosen from have error rest is easy you just have to check the ratio of error to find out everything. now if remainder in first step is (20,25) or (5,10) for 30.you now x in each case,put back every thing in original form. Now from 1st group take 2 coin from 1 pile and 3 coin from 2nd pile and 4 coins from another pile.similarly from all other groups except in 4th one change is that the pile from which you were taking 2 coins.take. 4 coins instead and weigh rest is easy just observe the ratio of error and find everything you want.now if remainder is (10,15) it is clear that counterfeit coins are in the 3rd or 4th group .from 1st group take 2 coins from 1 pile and 3 from another and 4 from another.similarly from rest except 3rd group where you have to take 3 coins from pile where you have to take 4 if remainder remains same or decrease and is between (10,15) ten x is quotient if remainder increases then x is quotient +1 and rest is easy just use ratio of error to find your answer.if remainder is (15,20). Use the previous arrangement if remainder is same or increase you now x is quotient +1 else it is quotient and rest is easy use ratio of remainders .
Note I have not written too obvious things .i could not find close brackets so understand it yourself.if you could not understand once try again.
At last I deserve a giant present.finally relaxing time. Thanks.

He halved every pill and ate one half of every pill

Cook .a killer would not have let her write something.if he was present at that moment.she was poisoned .cook was involved.

8 attempts.first at 8 if broken then 1 to 8 .if not broken then 15 if broken then try 9 to 14 if not broken then 21 .series go like,8 ,8+7,8+7+6,……………

He will remember the time he saw the ship.thenhe will get to that position then. He will estimate the distance the pirate ship have gone from this point as he have relation in speeds.now assume a thief is running with speed v and  is at distance x on linear  line and policeman at 2v then the distance at witch police man will catch up is r.now back to case, he will go in any direction with speed 2v(assuming v of pirate ship) and cover distance r.then he will turn 90 degree and move in a spiral out wards with pirate ship’s known point at centre and with speed v along the radius away from centre.i am not physics person so sorry for not knowing technical terms.

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Yo! That was one tough cookie .Although I chewed it finally

can’t be done unless it is exactly 24 hrs not within 24 hrs

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He will go till the start of 119th cable testing every oneand test it and las t one will be checked by telephone exchange