Cuberoot formation

Following puzzle from edex supplement-

Find a positive integer such that if its last 3 digits are removed,we get its cube root

Three boxes with marbles

This is one of the puzzles included by Martin Gardner in a book containing various puzzles.-
Imagine that you have 3 boxes one containing 2 black marbles,one containing 2 white marbles,the 3rd containing one black and one white marble -labelled BB,WW, and BW respectively.Someone switched the labels so that every box is incorrectly labelled.You are allowed to take one marble at a time out of any box without looking inside and by this process of sampling you are to determine the contents of all 3 boxes.What is the smallest number of drawings needed to do this? 

Completing a sequence

Here are six numbers in sequence.You have to find the next 2 numbers-
202    122   232   425  262  728

Pell equations

An equation of the type p^2-Nq^2=1 has been classified as Pell equation though it did not evolve from Mr Pell.
Given any value of N,one can find the values of p and q which satisfy this equation.
I have done extensive research on the subject ,finding the values of p and q for very many values of N-almost all upto 99 and some more values above 100.
There is a method for finding the solutions and this was used by me.
For values of N just above or below a perfect square the procedure does not require many steps but for values like 53,73 of N more steps were needed
As a variation for some values of N,you can get a solution for the alternative equation p^2-Nq^2=(-)1 after a few steps but will need more steps for p^2-Nq^2=1.
Examples -
N=24-solution p=5 q=1,more solutions can be found later like p=49,q=10
N=26......p=51q=10...p=5201,q=1020
N=48....p=7,q=1....p=97,q=14
N=50...p=99,q=14
N=53...p=66249,q=9100...This  number N has solution p=182 q=25 for the alternative equation involving the final result as (-)1

Shopper puzzle

Three items in a store are priced at USD 4.00   ,0.50    and,0.25
A person purchases 20 items paying a total of 20 dollars.
How many items of each did he buy?

Who paid for drinks

At one time the Canadian and US dollars were discounted by 10 cents on each side of the border i.e a Canadian dollar was worth 90 US cents in the US and a US dollar was worth 90 Canadian cents in Canada. A man walks into a bar on the US side of the border,orders 10 US cents worth of beer ,pays with a US dollar and receives a Canadian dollar in change.He then walks aross the border into Canada,orders 10 Canadian cents of beer,pays with a Canadian dollar and receives a US dollar in change.He continues this throughout the day, and ends up with the original dollar in his pocket.Who has paid for the drinks he has consumed?

Children weighing themselves-Rejoinder

This is a rejoinder regarding the issue of 5 children weighing themselves two at a time to reduce the ..expenses.The weights revealed by the weighing machine in ascending order were 51.7    52    53.5  54   55   55.3   55.8   56.7   57 and 58.5.You were asked to determine the individual weights
.
If the individual weights were a,b,c,d and e the combinations 2 at a time possible are a+b,a+c,a+d a+e,b+c,b+d,b+e,c+d,c+e and d+e Adding all 10 values will result in the sum 4(a+b+c+d+e).So a+b+c+d+e=(51.7+52+53.5+54+55+55.3+55.8+56.7+57+58.5)/4=549.5/4=137.375.Deducting a+b=51.7 and d+e=58.5 we get c=27.175.We can then find that a=24.825,b=26.875,d=28.675 and e=29.825 

Conversation logic-Rejoinder

Since no one lies on Sundays and A says he does so in his second statement,it means he is lying.His first statement is also therefore false.Hence A lies on Mondays,Tuesdays and Wednesdays and B lies on Thursdays,Fridays and Saturdays.Since A and B do not lie on the same day,it means B is telling the truth.Since B lies on the next day as stated by him,the day of the conversation is Wednesday. 

Children weighing themselves

Five children thought of a scheme to weigh themselves on an automatic weighing machine at the cost of a single coin.Two of them got on to the stand at the same time,and one of them changed places with another until all the ten pairs are weighed..The results in kgs were as  follows-51.7..  52    53.5   54     55    55.3      55.8     56.7     57    and  58.5...What are their individual weights?

A Conversation logic

This is a logic puzzle for you
Out of 2 persons A and B,A lies on Mondays,Tuesdaysand Wednesdays and tells truth on other days.B lies on Thursdays,Fridays and Saturdays and speaks truth on other days.
At noon on a particular day the following conversation took place-
A-I lie on Saturdays
B-I will lie tomorrow
A-I lie on Sundays
On which day of the week this conversation took place?
  

Cryptogram for deciphering-Rejoinder

The sentence starts with  number 26.As A and I are the only single alphabet words,26 can stand for for alphabet   A or  I.By logic we can start the numbers 26,25,24 etc with A,B,C etc or I,J,K etc or I,H,G etc or A,Z,Y etc.
By seeing all these options we can decipher the sentence.It is actually as follows-
A bird in the hand is messy.,

Sequence filling puzzle

There was a puzzle shown in Sunday Magazine New Indian Express 20 july 2014 as follows-
What number comes next in the sequence 1,4,5,6,7,9,11..
Although I can give a hint that it is an alphanumeric sequence (Having connection with numbers and  alphabets) -it was truly  difficult to find the answer.
You will be surprised the next number is 100.
All the numbers shown in the puzzle when expressed in words do not contain the alphabet T.
The only next number with this quality as you can observe will be 100..

Birthdays for twins-Rejoinder

This is with reference to my earlier blog where I had enquired how the younger child among twins could celebrate his birthday earlier than his older brother.
This is possible as per  the circumstances shown below-
At the time the mother went into labour,she was travelling east-bound by boat.The older twin was born first early on March 1st,The boat then crossed the international date-line (where the date  still relates to February 28th) and the younger twin was born at that time viz on February 28th.
In a leap year the younger twin will thus celebrate his birthday 2 days before his elder brother.

Cryptogram for deciphering

A cryptogram was published in Times of India paper of October 1st
A series of numbers were given,each number referring to a particular English alphabet and the whole group supposed to represent a message.
Following are the numbers
26,25,18,9,23,18,13,7,19,22,19,26,13,23,18,8,14,22,8,8,2
Unfortunately no hint was given about the number  of words involved and the number of alphabets included in each word.It was thus  difficult to decipher the message.
Let me give you this hint
There are 7 words and they are represented by the following group of numers .
26....... 25,18,9,23....18,13.....7,19,22.....19,26,13,23....18,8.....14,22,8,8,2
Can you now decipher the message
The highest number is 26 and the numbers from 1 to 26 are supposed to refer to the 26 alphabets in a particular order  like a,b,c.d,e....... or z,y,x,w,v etc

Identification of an odd ball out of twelve

You have 12 identical balls.All of them weigh the same except one odd ball weighing either higher or lower than the other 11.You have a pan balance with no weights.In 3 weighings find the odd ball out and determine whether it weighs higher or lower than the others. 

Group of 8 numbers-Rejoinder

Only one member-Shekar- could send an answer which was correct
The answer is that the 8th number is 25
This is arrived at as follows-
The average of the first 2 being 15.5 their total is 31.
The average of the next 3 being 64/3 their total is 64.
The average of all the 8 numbers being 20,their total is 160.
Thus the total of the last 3 should be 160-31-64=65
If the 6th number is denoted by 'x' the 7th and 8th numbers will be (x+4) and (x+7)
So their total will be x+(x+4)+(x+7)=3x+11.
Equating this to 65 we find x,the 6th number is (65-11)/3=18
Hence the 7th and 8th numbers are 22 and 25  

Bookworm's travel

Here is a puzzle-
A bookworm eats from the first page of an encyclopedia to the last page.The bookworm eats in a straight line.The encyclopedia consists of ten 1000 page volumes and is sitting on a bookshelf in the usual order Not counting covers,title pages etc how many pages does the bookworm eat through?
Dont say it is easy- it eats through 10000 pages.
It actually eats through 8000 pages.Remember when the encyclopedia is in the correct order on the shelf,the first volume is on the left.so the first page is not on the extreme left.So also the last page is not at the extreme right.Thus only the middle 8 volumes consisting of 8000 pages has been travelled through..

Tropical fruit in an open truck-rejoinder

This refers to my earlier blog same title
As the water content out of the total weight 1000kg  earlier was 99%,the weight of the fruit content should have been 1% or10 kg.After the transit period,the water content was stated to be 98%.That means the fruit content then became 2%.As the fruit content did not suffer in weight the earlier 10kg remained intact.As this constituted 2% of the total weight,the total weight of the fruit should now be 500 kg.   

Selection/deletion of numbers-Rejoinder

This is with reference to  my earlier blog with same title-
I had mentioned that from all numbers from unity upwards,you should delete multiples of 3 and those that contain 3.
There are 3 groups of numbers which need deletion-
(a)Multiples of 3
(b)Numbers between 30-39 excluding those under a)
(c)Other numbers like 23,43,53,73,83 etc
Let us consider numbers upto 80.
There are 26 multiples under category (a)
Under category (b)there are 6 numbers viz 31,32,34,35,37and 38.
Under category (c)we have 5 numbers viz 13,23,43,53 and 73.
Thus the remaining numbers (among those upto 80) are 80-26-6-5=43.
The 40th number is thus 76 excluding 80,79 and 77.
Considering numbers beyond 80,we have 82,85,86,88,89,91,92,94,95,97,98,100 etc,As there were 43 numbers upto 80,the total numbers upto 100 will be 55.-The 50th number is thus 92 excluding the 5 numbers 100,98,97,95 and 94.-.
Let us next consider multiples of 4 and those containing 4 out of these 55 numbers which are to be deleted.
These are- 4,8,14,16,20,28,40,41,44,46,47,49,52,56,64,68,74,76,80,88,92,94 and 100 viz a total of 23 numbers(16 multiples of 4 and 7 others containing 4-viz 14,41,46,47,49,74 and 94
The remaining numbers (among all numbers upto 100 are thus 55-23=32.
We have to go beyond 100 using these algorithms to get further numbers which would remain.

Tropical fruit on an open truck

 A farmer is taking 1000kg of a tropical fruit which contains 99 percent water for sale in an open truck.Due to being held up midway  and sun being hot  the water content of the fruit comes down to 98 percent .What is the weight of the fruit now?