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Topic: Numbers juggling
Message: Posted by: stanalger (Jun 14, 2005 01:10PM)
No, I'm not posting in the wrong forum; I'm
sharing one of my original puzzles:

This one should be solved by hand (pencil and paper).
If you use computer software, you will be cheating
yourself out of a pleasant surprise.

Examine the following sum:


Math challenge: Produce a one-to-one correspondence between
the elements of the set {0, 1, 2, 3, 4, 5 ,6 ,7 ,8 ,9} and
the elements of the set {C, L, U, B, S, N, A, M, E, R}
so that when each letter in the sum is replaced with its
corresponding digit, the result will be a valid base ten
sum of two six digit numbers.

Word challenge: Unscramble the ten different letters
used in the sum to spell a familiar ten-letter word.

If you've solved both parts, post your solution to the
word challenge in encoded form via the one-to-one
correspondence which solves the math challenge.

**Please do not post partial solutions.**


For those not familiar with the jargon of the jugglers,
"numbers juggling" once referred to the juggling of 5
or more objects. As more and more jugglers (both
professional and recreational) became more and
more proficient at keeping more objects
in the air, the definition of "numbers juggling"
began to change. Many ball jugglers didn't
consider ball juggling to be "numbers juggling"
unless at least 7 balls were involved. Juggling
5 clubs was still considered "numbers juggling"
because juggling 5 clubs is more difficult
than juggling 5 balls.

And the jugglers continue to push the boundaries.
Today, many would argue that "numbers juggling"
should be reserved for 8 or more balls...and
6 or more clubs.

It's certainly safe to say that most jugglers
would agree that 9 balls or 7 clubs
should still be considered "numbers juggling."

Stan Alger
Message: Posted by: TomasB (Jun 14, 2005 03:22PM)

I must say that I missed the pleasant surprise but with all those things fitting together this puzzle seems like it was meant to be and I can't fathom how you came up with it. Absolutely unreal work, Stan.

Message: Posted by: stanalger (Jun 14, 2005 03:45PM)
Congratulations, Tomas! You made quick work of that one.

I suppose this thread is finished. No need for any further posts.
If any other would-be solvers get frustrated with a pencil and paper
attack, anagram software (or an anagram dictionary) together with
your 10 digit number will provide all answers.

Message: Posted by: stanalger (Jun 22, 2005 06:20PM)
But software/dictionary should only be used as a LAST RESORT.
Message: Posted by: leonard (Jun 28, 2005 10:33PM)

Nice puzzle. Thanks. I hadn't worked a cryptarithm in years. I would nominate


as an alternate to Tomas's solution.

Message: Posted by: stanalger (Jun 29, 2005 08:31AM)
A second solution? Very good, leonard...and shame on me!
I [b]thought[/b] I had been thorough in my search for
solutions; obviously I was mistaken.

I came up with this puzzle in the early 80's. It was
published in _Juggler's World_. Leonard, you are the
first to point out the non-uniqueness of the "solution."

At about the same time, I came up with another cryptarithm
with a juggling theme. It didn't have the added bonus that
the letters could be rearranged to spell a ten-letter word,
but I think it [b]does[/b] have a unique solution.

If the solution isn't unique, I'll bet leonard will find
the alternate solution(s).

Here it is: I * JUGGLE = PLATES

(Juliet: Gasp! I must be spending too much time thinking
about Stephen Buxton's puzzles. These ten letters also
include P I E as well as P L A E. See Buxton's "Holiday
Facts" and "Doors, Part Three.")

Stan Alger
Message: Posted by: leonard (Jun 30, 2005 10:45AM)
I obtained only one solution this time (to the new puzzle). If I am correct, JUGGLE has 839 as a divisor.
Message: Posted by: stanalger (Jun 30, 2005 11:12AM)
Thanks, leonard.

Now I feel more confident that
has a unique solution.

My solution is buried in my apartment.
(Water was leaking from the apartment
above mine, so I had to quickly
consolidate the contents of the
wet rooms into the dry rooms.
The dry rooms have boxes stacked high.
Been living this way for several weeks
now. Can't wait to get things
back to normal.)