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?

More rectangular magic grids

In continuation of my previous blog,I am showing below bigger magic rectangular grids
1)3 rows/5 columns-Total each row 50,Total each column 30
First row-       1     17     2     16    14
Second row    9     10    21     6      4
Third row       20     3     7       8     12...Numbers from 1 to 21 with 5,11,13,15,18,19 avoided
You need a total all rows or all  columns 150.This total can be obtained by using the 15 numbers from 3 to 17. .Can you work up a rectangle using those numbers?
2)4 rows/5 columns-Total each row 60,Total each column 48
First row         1      13    24    5      17
2nd row          23     4      6     7      20
3rd row          15    12    16   14       3
4th row           9      19     2    22      8.....Numbers from 1 to 24 with 10,11,18,21 avoided
3)In the example above you needed a total all rows or all columns 240.As a variation I tried using the 20 numbers from 1 to5 and 8 to 22.
The grid is like this-
 First row            1      21   16    18     4
2nd row            11     12    3     15    19
3rd row             14     13   20     5      8
4th row              22      2     9    10    17

Rectangular Magic grid

This is similar to a magic square.I am presenting a rectangular grid with 2 rows and 3 columns.
Each row contains 3 numbers and the sum of the numbers in each row is the same
Each column contains 2 numbers and the sum of the numbers in each column is the same
No number gets repeated anywhere.
Following are 2 examples-
1)First row-..........1      8      9
   Second row......11     4      3..   Each row totals 18 and each column totals 12
2)First row......................................1      10     7
    Second row................................11      2     5.....similar to 1) above

I am also giving 2 examples of rectangular grids with 4 numbers in each row and 3 numbers in each column
1)........1      4     15    12
           5      11    6      10
          18      9     3       2....     each row total 32 each column total 24
2)                                       1       4       11     16
                                          9.      7        10     6
                                         14      13       3      2     similar to previous example
You can make such rectangular grids easily with large numbers but it is difficult if you use small numbers
You can also have more numbers each row and more numbers each column

Puzzle about 3 variables a,b,c

Three variables are governed by the relation a^2+b^2=c^2
Can you find which of the following is true?
1)(a+b)=c
2)(a+b)>c
3)(a+b)<c
You have to explain your reasoning.

Selection /Deletion of numbers

Suppose I first make a list of all the consecutive numbers from unity.
Suppose next I delete all the numbers which contain the digit 3 as well as those which are multiples of 3.
From the list of the remaining numbers,can you tell me what will be  the 40th number or the 50th number?
Suppose I next also delete from this new list all numbers containing the digit 4 as well as multiples of 4.
What will be the 30th number now? 

Group of 8 numbers

The average of the 8 numbers forming a group is 20.The average of the first 2 numbers is 15.5 and the average of the next 3 is 64/3.If the 6th number is less than the seventh and eighth by 4 and 7 respectively,find the 8th number

Birthdays for twins

Here is a puzzle for you-
A mother gives birth to two boys as twins.
The younger twin should normaly celebrate his birthday later than his older twin brother.
In a prticular case however the younger twin celebrates it earlier.
How is it possible?