Cryptarithmetic Problems
John Yeadon
Can anyone solve these five cryptarithmetic puzzles.
S M I T H S + Q U I C K = T R I C K S
C R O S S + R O A D S = D A N G E R
A + M E R R Y + X M A S = T U R K E Y
L Y N D O N * B = J O H N S O N
L Y N S E Y / D E = P A U L
NB: Within each puzzle, each letter consistently substitutes for a
decimal digit and there are no leading zeros.
Have you any more of this ilk?
il...@isgtec.com
In article <356c9b9b...@news.compuserve.com>,
SPOILER
Here are computer generated solutions:
SMITHS + QUICK = TRICKS
Solution number 1:
436584 + 79620 = 516204
Solution number 2:
476584 + 39620 = 516204
CROSS + ROADS = DANGER
Solution number 1:
96233 + 62513 = 158746
A + MERRY + XMAS = TURKEY
Solution number 1:
2 + 97445 + 6928 = 104375
LYNDON * B = JOHNSON
Solution number 1:
570140 * 6 = 3420840
LYNSEY / DE = PAUL
Solution number 1:
609450 / 75 = 8126
__/\__
\ /
__/\\ //\__ Ilan Mayer
\ /
/__ __\ Toronto, Canada
/__ __\
||
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Glenn Rhoads
John Yeadon wrote:
> Can anyone solve these five cryptarithmetic puzzles.
>
> [puzzles deleted]
>
>> Have you any more of this ilk?
Plenty.
THIS + ISA + GREAT + TIME = WASTER
FATHER + MOTHER = PARENT
EARTH + AIR + FIRE + WATER = NATURE
CALL + 1800 + 2385355 + FEDERAL = EXPRESS
ADAM + SAYS + YES + IM + ADAM = MADAM
THIS + IS + VERY = EASY
NEIL + A. + SEES = ALIEN (also a palindrome!)
DOUBLE + DOUBLE + TOIL = TROUBLE (from Shakespeare)
MAD * MAN = ASYLUM
COGITO = ERGO * SUM
FERMAT * S = LAST + THEOREM.
WINNIE / THE = POOH
THREE + THREE + ONE = SEVEN
ONE + THREE + FOUR = EIGHT
SIX + SIX + SIX = NINE + NINE
SEVEN + SEVEN + SIX = TWENTY
FORTY + TEN + TEN = SIXTY
MAKE + A + NEW + PLAN = STAN
HOP + ON + THE + BUS = GUS
DONT - NEED - TO - BE - COY = ROY
FEET feet = INCHES inches (i.e. FEET * 12 = INCHES)
THREE is a prime number, FOUR is a perfect square, EIGHT is a perfect cube.
In the next section, X could be any digit
*****************************************
xx8xx
__________
xxx ) xxxxxxxx
xxx
---
xxxx
xxx
---
xxxx
xxxx
----
(despite its formidable appearance, the above can be solved with
almost no trial and error)
XXX * XX = XXXXX (each digit is a prime number, and only one solution)
PUZZLE
* xxxxxxx
-------
xxxxxxx
xWxxxxx
xxOxxxx
xWORLDx
xxxxLxx
xxxxxDx
xxxxxxx
-------------
xPxUxZxZxLxEx
xxx
* xxx
-----
xxx
xxx
xxx
---------
xxxxx
(In the above, no digit appears more than twice. Only one solution!)
In the believe it or not category, we have cryptarithms in the form
of a haiku, a poem, and a chess game!
************************************
a haiku
-------
IN + ARCTIC + TERRAIN
+ AN + ANCIENT + EERIE + ICE + TRACT
+ I + ENTER + A + TRANCE = FLATIANA
A poem about Sevvoth Island in the North Sea
--------------------------------------------
TEN + HERONS + REST + NEAR + NORTH + SEA + SHORE
+ AS + TAN + TERNS + SOAR + TO + ENTER + THERE
+ AS + HERONS + NEST + ON + STONES + AT + SHORE
+ THREE + STARS + ARE + SEEN
+ TERN + SNORES + ARE + NEAR = SEVVOTH
P-K4 + P-K4
+ N-KB3 + N-QB3
+ B-B4 + N-B3
+ P-Q4 + PxP
+ O-O + P-Q3
+ NxP + B-K2
+ N-QB3 + O-O
+ P-KR3 + R-K1
+ R-K1 + N-Q2
+ BxP + KxB
+ N-K6 + KxN
+ Q-Q5 + K-B3
+ Q-KB5 = BOOHOO
Notes: The - and x are symbols representing a digit. The O in the castling
moves O-O are Ohs not zeroes. Be sure to check out the game!
Hats off to whoever came up with this "chessarithmic."
I have some more and I'm sure others do as well but this should be
enough to satisfy for quite some time.
J. Moran
In article <356c9b9b...@news.compuserve.com>, JohnY...@Compuserve.com
(John Yeadon) wrote:
> L Y N S E Y / D E = P A U L
> Have you any more of this ilk?
How about
'merry xmas to all'
each word is a square (maybe two answers but
if so I can't find the other!)
Scouse!
--
_____________________________________________
WWW.argonet.co.uk/chessnorth /
Ł3000 + Prizes at Aintree /Internet access for Chess in the North West
/ Email - mor...@argonet.co.uk
__________5-7 June________/
cod...@my-dejanews.com
In article <na.a906bf484f...@argonet.co.uk>,
J. Moran <mor...@argonet.co.uk> wrote:
>
> In article <356c9b9b...@news.compuserve.com>, JohnY...@Compuserve.com
> (John Yeadon) wrote:
> > L Y N S E Y / D E = P A U L
> Snip
> > Have you any more of this ilk?
>
> How about
>
> 'merry xmas to all'
> each word is a square (maybe two answers but
> if so I can't find the other!)
> Scouse!
27556 3249 81 400
34225 7396 81 900
All I find. Don't think I missed any.
CO
Torkel Franzen
J. Moran <mor...@argonet.co.uk> writes:
> 'merry xmas to all'
> each word is a square (maybe two answers but
> if so I can't find the other!)
There are two solutions, found in 650 ms on a Sparc 5:
| ?- solve(M,E,R,Y,X,A,S,T,O,L).
A = 4,
E = 7,
L = 0,
M = 2,
O = 1,
R = 5,
S = 9,
T = 8,
X = 3,
Y = 6 ? ;
A = 9,
E = 4,
L = 0,
M = 3,
O = 1,
R = 2,
S = 6,
T = 8,
X = 7,
Y = 5 ? ;
no
Caspa
Glenn Rhoads <rho...@living.rutgers.edu> wrote in article
<6krefo$jpb$1...@living.rutgers.edu>...
> John Yeadon wrote:
>
> > Can anyone solve these five cryptarithmetic puzzles.
> >
> > [puzzles deleted]
> >
>
[snip]
> I have some more and I'm sure others do as well but this should be
> enough to satisfy for quite some time.
>
Hey, has anyone tryed doing these in base 12? Maybe someone could come up
with one. If no-one else does, I might try, but I don't know how -- I've
hardly ever tried the base 10 ones!
Caspa.
ceetec.s...@gmail.com
Richard Heathfield
> SEND+MORE=MONEY
spoiler for hint
spoiler for hint
spoiler for hint
spoiler for hint
spoiler for hint
spoiler for hint
spoiler for hint
I've worked this out, but I don't want to publish the answer. I thought,
however, that I might publish a very, very easy hint, in case anyone
needs a hook into this.
First, the rules (which the OP has not specified, but cryptarithm rules
are pretty standard):
Each different letter stands for a different digit. If the same letter
is used twice, the same digit is meant in each case.
Although a digit can be 0, no /leading/ digit can be 0. Thus, in the
current example, we know that neither S nor M is 0.
The sum has to work. That is, when you plug in the digit values into
SEND+MORE=MONEY the sum has to come out right. If we ended up with
1234+5672=58329 we'd know something was wrong, because adding those two
numbers doesn't give that result.
Okay, now for the partial hint.
The maximum sum of two four-digit numbers is 9999+9999=19998. SEND
cannot be as high as the maximum, and neither can MORE. So what possible
candidates are there for the digit corresponding to M? (Bearing in mind
that leading 0s are not allowed, so neither S nor M can be 0.)
Another partial hint:
D + E = Y (modulo ten).
So we know that neither D nor E is 0.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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