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.