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| Title: | Mathematics at DEC |
|
| Moderator: | RUSURE::EDP |
|
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
46.0. "Doubly true alphametics" by HARE::STAN () Sun Feb 26 1984 00:13
A doubly-true alphametic is an alphametic where the words
themselves satisfy the stated equation. For example, the
base 7 alphametic:
T W O
+ T W O
-------
F O U R
has the unique solution 523+523=1346 in base 7, and also
represents the fact that 2+2=4.
Doubly-true alphametics have been appearing recently in the
literature. I decided it would be neat to find all double-true
alphametics of certain classes. Now you understand the reason behind
the last two notes.
Anyhow, I have run a program that searches for doubly-true
alphametics consisting of the sum of two numbers being a third,
all three numbers in the range 1-20. Only doubly-true alphametics
that have a unique solution are permitted. I searched 14 different
languages. All bases from 3 through 16 were searched.
The results are listed in the first response to this note.
[I will probably submit this to some journal.]
Of interest is the fact that there was only one solution in English
(TWO+TWO=FOUR in base 7) and only one solution in base 10 (EINN+EINN=TVEIR
in Icelandic).
I am also working on other studies, such as addition alphametics
with more than two summands, and certain sums with numbers up to 100.
I will report on these later.
| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 46.1 | | HARE::STAN | | Sun Feb 26 1984 00:13 | 252 |
| Dutch. Base 6:
een 114
drie 2501
---- ----
vier 3015
English. Base 7:
two 523
two 523
---- ----
four 1346
French. Base 8:
cinq 4627
siz 361
---- ----
onze 5210
German. Base 5:
ein 234
ein 234
---- ----
zwei 1023
German. Base 6:
zwei 2153
zwei 2153
---- ----
vier 4350
German. Base 7:
zwei 3102
zwei 3102
---- ----
vier 6204
German. Base 8:
ein 567
ein 567
---- ----
zwei 1356
German. Base 8:
funf 1721
funf 1721
---- ----
zehn 3642
German. Base 9:
vier 4325
funf 1861
---- ----
neun 6286
Hungarian. Base 5:
ot 41
ot 41
--- ---
tiz 132
Icelandic. Base 8:
einn 7355
einn 7355
----- -----
tveir 16732
Icelandic. Base 9:
einn 4677
einn 4677
----- -----
tveir 10465
Icelandic. Base 10:
einn 7366
einn 7366
----- -----
tveir 14732
Icelandic. Base 11:
einn 6899
einn 6899
----- -----
tveir 12687
Italian. Base 5:
uno 104
uno 104
--- ---
due 213
Italian. Base 6:
uno 105
uno 105
--- ---
due 214
Italian. Base 7:
tre 312
tre 312
--- ---
sei 624
Italian. Base 9:
uno 632
otto 2552
---- ----
nove 3284
Norwegian. Base 4:
en 12
en 12
-- --
to 30
Norwegian. Base 6:
to 25
tre 241
--- ---
fem 310
Norwegian. Base 6:
fire 1520
fire 1520
---- ----
atte 3440
Norwegian. Base 7:
tre 534
tre 534
---- ----
seks 1401
Norwegian. Base 7:
fire 2150
fire 2150
---- ----
atte 4330
Polish. Base 6:
tszy 3105
tszy 3105
----- -----
szesc 10214
Portuguese. Base 7:
um 43
dez 652
---- ----
onze 1025
Portuguese. Base 7:
seis 2432
seis 2432
---- ----
doze 5164
Portuguese. Base 8:
um 62
dez 753
---- ----
onze 1035
Portuguese. Base 9:
cinco 52458
oito 8268
----- -----
treze 61737
Romanian. Base 5:
uan 234
uan 234
---- ----
doua 1023
Romanian. Base 8:
uan 567
uan 567
---- ----
doua 1356
Romanian. Base 8:
doua 5342
doua 5342
----- -----
patru 12704
Spanish. Base 5:
un 24
un 24
--- ---
dos 103
Spanish. Base 6:
un 32
un 32
--- ---
dos 104
Spanish. Base 7:
seis 2432
seis 2432
---- ----
doce 5164
Spanish. Base 8:
dos 653
ocho 5415
---- ----
diez 6270
Swedish. Base 7:
tre 312
tre 312
--- ---
sex 624
|
| 46.2 | | HARE::STAN | | Tue Apr 17 1984 23:23 | 2 |
| Peter Gilbert has confirmed these results with an independent
computer program.
|
| 46.3 | | XENON::GAUDREAU | | Wed Jul 11 1984 12:56 | 7 |
| .re #1 french entry,
5 + 6 = 11, I thought "SIX" was french for the numeral 6. I've been using
it that way for several years now. "SIZ" is new to me...
Joe
-=-
|