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.

1 comment:

  1. Nice :-) I created my two sets following your logic.
    2576,6483,7143....4285,7394,4523

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