Re: Enigma 1400 - Memory PIN

"Chappy" <petergregorychapman@xxxxxxxxxxx> writes:
Enigma 1400 - Memory PIN
New Scientist magazine, 15 July 2006.
by Adrian Somerfield.

My bank has just issued me with a new
five-digit PIN. I find it hard to
remember these things, but I have
discovered how to recall this one. [...]
the first two digits form a perfect
square

6 choices.

and the last two form another,
smaller perfect square,

combines for 15 choices.

while the central
digit is the smallest digit present.

So 16 and 81 are out. So there are only 6 choices of squares,

Each
of the five digits is different,

Make that 4 choices, as 64 doesn't play well with most
other squares. Only 1 of those admits 2 choices for
a middle digit, for 5 in total.

36125
49125
49136
49236
64125

If
I arrange the five digits in every
possible different order to form
different numbers and add all these
numbers together,

You mean "if you take the digit sum, and multiply by 24*11111".
The digit sums are 17, 21, 23, 24, 18.

These yield 4533288, 5599944, 6133272, 6399936, 4799952

I get a large number
which consists of a palindrome, every
one of whose digits is a multiple of 3.

The 4th of the 5 then.

What is my PIN?

Far too easy.

Phil
--
"Home taping is killing big business profits. We left this side blank
so you can help." -- Dead Kennedys, written upon the B-side of tapes of
/In God We Trust, Inc./.
.

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