Monday 30 January 2012

More cases-Digits being the same

This has reference to my earlier blog title-Digits being the same.
I am giving below another group of 5 digits from among the digits from 0 to 9-
8,6,5,4,1-
You can frame 4 different numbers from these 5 digits,which on doubling will give you 4 numbers formed out of the digits 9,7,3,2,0.
One example is 14865 which on doubling will give you 29730.
Can you find the remaining 3 numbers?


Tuesday 24 January 2012

Question N-1(Black hole number 123)

Let me pose a question reg black hole number 123.,referred to in my earlier blog.
Suppose you take a number containing  all odd digits or all even digits..
Do you  think the situation will hold good?
Supposing also there are one or more zeros.How should you count these zeros viz whether as even or odd?
Test a few cases and find the answers.

Tuesday 10 January 2012

Two sets of 6 digit numbers

Let me present two sets of 6 digit numbers-with 3 numbers in each set-which show a surprising feature.
The numbers are
123789,561945,642864...........242868,323787,761943.The totals of the numbers in each set is the same.
Now remove the first digit in each no in each set.The totals of the 5digit numbers in each set will be the same.
Continue the process of removing the first digits till you reach single digit numbers.The total of the numbers in each set will continue to be the same.
This is not the only surprising feature.
You can remove the last digit in each number(instead of the first digit).The totals of the new 5digit,4digit...single digit numbers will continue to be the same.
You want another surprise! Instead of adding the numbers,you can add the squares of the numbers The totals will continue to be the same.I will only show for example the position when the numbers are brought down to 2 digit numbers and single digit numbers.
89+45+64=198=68+87+43.....9+5+4=18=8+7+3.
12+56+64=132=24+32+76....2+6+4=12=4+2+6.
For squares the totals are  122 and 56  considering only single digit cases.

Tuesday 3 January 2012

Joining digits and making numbers

Let me present two groups of 3 digits each which can be used for making numbers having a surprising property.
First group the digits are 4,5 and 6.They make a total of 15 and their squares make up a total of 77.
Second group -the digits  are  8,3 and 2 giving the total of 13 ,but giving the same total 77 relating to the squares.
You can join one digit from the first group (say 4) with a digit from the second group (say 8) making the numbers 48 or 84.You can similarly join other digits one from each group.- making 6 more 2 digit numbers.The surprising fact is that you will have again two groups of 3 numbers each,each number consisting of 2 digits and the squares of the numbers each group making the same total.-shown below for ready perusal-
The notation S refers to the squares of the numbers involved-
S48+S53+S62=S84+S35+S26=8957
S48+S52+S63=S84+S25+S36=8977
S43+S58+S62=S34+S85+S26=9057
S43+S52+S68=S34+S25+S86=9177
S42+S58+S63=S24+S85+S36=9097
S42+S53+S68=S24+S35+S86=9197