Here you have a sample of
92 cryptarithms retrieved from journal Sphinx, 1933-34 editions. The answers to these problems are given at the
end of this page.
We are grateful to Jean-Pierre Le Franc (from
Cesson-Sevigne, France) for lending us the Sphinx
magazines from his private collection, where these puzzles
were taken from. Thanks are also due to Evelyne Weiser for
introducing us to Jean-Pierre's Sphinx collection.
Sphinx cryptarithms were either contributed by M. Pigeolet or
otherwise submited by the subscribers to the magazine. To
boost interest on cryptarithmetic, Sphinx editors used to
organize puzzle contests paying cash prizes to the winners.
Along the year 1933 they were running "The
Cryptarithmetic Year" competition, followed by "The
Cryptarithmetic Key" in January 1934.
Enjoy these old precious
jewels of the cryptarithmetic art !
From
Sphinx,
with love !
1) Sphinx - Jan 1933 - Page 7
By M. Pigeolet
Reconstruct the multiplication, in which all the A=3 are given.
. . . . . A
A . . . . . .
---------------
A . A . A . J
. . . . . A
. . . A . . N
. . . A . V
. A . . . . I
. . . . . A E
J A N V I E R
---------------------------
. . . . . . . . . . . . .
2) Sphinx - Jan 1933 #115 - Page 9
By M. Van Esbroeck
A B C = C4, B C A = D4
3) Sphinx - Jan 1933 #116 - Page 9
By M. de Ville (Namur)
F A G = E × H B I,
F A G is formed from 3 consecutive digits.
4) Sphinx - Jan 1933 #11 - Page 14
By M. Pigeolet
Ten cubes in stairstep:
x
x
x
x x x x
x
x
x x x x
x
x
x x x x
x
x
x x x x
x
x
x x x x
5) Sphinx - Feb 1933 #120 - Page 26
By M. Lapierre
Reconstruct the extraction of square root.
* * A B
-----------------
\/ * * * * * * * *
* *
-------
* * *
A * *
---------
* * * *
B * * *
-----------
* * * *
* * * *
-------
6) Sphinx - Feb 1933 #121 - Page 26
By M. de Ville (Namur)
K E D = E × G B,
K E D is formed from three consecutive digits; G B is formed
from two consecutive digits.
7) Sphinx - Feb 1933 #122 - Page 26
By M. Rose-Innes (Yokohama)
A printer, setting up the following division, found that he had only type numbers
7 and 0 which he put in their respective places, and two A's, which he used to
substitute for a certain digit that appears twice in the dividend; but this same
digit was next replaced by asterisks in all other parts of the division. The divisor
is equal to the quocient.
* * *
------------
* * * | A * * * 7 A
* * 0 *
---------
* * * 7
* * * *
---------
* * * *
* * * *
-------
0
8) Sphinx - Feb 1933 - Page 28
By M. Pigeolet (Anvers)
Reconstruct the division.
. 6 . . . .
--------------
2 8 | F E V R I E R
. .
-----
. . .
S I X
-------
. . .
. . .
-------
. . .
. . .
-----
0
9) Sphinx - Mar 1933 #125 - Page 44
By L. Martin (Paris)
Take three consecutive numbers: x, y, z.
ABC, ACB and ABC + ACB are the differences of the cubes
of x, y and z expressed in the equations:
ABC = z3 - y3; ACB = y3 - x3 and ABC + ACB = z3 - x3.
10) Sphinx - Mar 1933 #126 - Page 44
By M. Lapierre
Reconstruct the extraction of square root.
A A *
-------------
\/ * * * * * A
* *
-------
* * * *
* * * *
-----------
* * * * *
* * * * *
---------
11) Sphinx - Mar 1933 - Page 45
By M. Pigeolet
Reconstruct the multiplication.
A R . .
R A . .
----------
. . . . M
. . . . A
. . . . R
M A R S
-----------------
. . . . . . . .
12) Sphinx - Apr 1933 #130 - Page 60
By M. Lapierre (Wattrelos)
Reconstruct the extraction of square root.
* A B
-------------
\/ * * * * * *
* A
-------
* * *
* * B
---------
* * * * *
* * * * *
---------
13) Sphinx - Apr 1933 #134 - Page 60
By M. Pigeolet
ROME, PARIS, ARRAS, ARLON and LENS are five prime numbers.
NIMES, ANS, MONS each of them is a product of a prime by 7.
SPA is a square. What are these numbers ?
14) Sphinx - Apr 1933 - Page 61
By M. Pigeolet
Reconstruct the division.
P L S
-----------------
A V R I L | 1 . . 6 . . . .
A V R I L
-------------
. . . . . .
. . . . 1 6
-------------
. . . . . .
P A Q U E S
-----------
0
15) Sphinx - May 1933 #135 - Page 74
By M. Lapierre
Reconstruct the extraction of square root.
* B *
-----------
\/ * * * * A
*
-----
* * *
* *
-------
* * *
* * *
-----
16) Sphinx - May 1933 #136 - Page 74
By M. Pigeolet
Reconstruct the multiplication and the division.
Q U I
P R E N D
-----------
* * *
* * * *
* * *
* * *
-----------------
Ç A | * * * * * * * | * * * * * *
* *
-------
* * *
* * *
-------
* * *
* * *
---------
0
17) Sphinx - May 1933 - Page 76
By M. Pigeolet
MAI is the square of ST.
. . . . . A
M A I
--------------
. . . . . . .
. . . . . . .
. . E N . . .
-------------------
P R I N T E M P S
18) Sphinx - Jun 1933 #141 - Page 86
By M. Rose-Innes (Yokoama, Japan)
In the sum of the series 500 + 501 + 502 + ..... + 501010, it was found that 8
consecutive digits between the 1010th and the 990th terms (counting right to
left) can be represented by PIGEOLET. What are these figures and what
places they occupy ?
19) Sphinx - Jun 1933 #142 - Page 86
By M. Pigeolet (Anvers, Belgium)
The two words in the name of ROSE-INNES from Yokoama are squares,
while OR is a prime number. What are these numbers?
20) Sphinx - Jun 1933 - Page 89
By M. Pigeolet
Reconstruct the multiplication.
E T E
* * *
---------
* * 2 1
J U I N
* * *
-------------
* * 2 * * 1
21) Sphinx - Jul 1933 #146 - Page 105
By M. Rose-Innes (Yokohama, Japan)
Reconstruct the division.
* *
-----------
A B * | * * C D *
* * C E
---------
* F F *
* * E D
--------
D E *
22) Sphinx - Jul 1933 #147 - Page 105
By M. Lapierre
Reconstruct the extraction of square root.
B A *
-------------
\/ * * * * * A
* A
-------
* * * *
* * * C
-----------
* * * *
* * * *
-------
23) Sphinx - Jul 1933 #148 - Page 105
By W. F. Cheney (from American Mathematical Monthly)
The arithmetic mean of NED and SASH is SHUN. Their geometric
mean is SEND and their harmonic mean is SEED. Each letter stands
for a different digit.
24) Sphinx - Jul 1933 - Page 106
By M. Pigeolet
Reconstruct the extraction of square root.
* * * *
---------------
\/ J U I L L E T
*
---------
* * * * * *
* * * * * *
---------
* * * * * * * * *
* * * * * * * * *
---------
0
25) Sphinx - Aug 1933 #151 - Page 119
By M. Lapierre
Reconstruct the extraction of square root.
A A *
-------------
\/ * * * * * A
* *
-------
* * *
* * *
---------
* * * *
A * * *
-------
26) Sphinx - Aug 1933 - Page 125
By R. Man.
AOUT is a prime number, as well as its reverse TUOA.
A O U T T U O A
+ A T A O - U * T T
---------- ----------
T U * U O * T *
27) Sphinx - Sep 1933 #156 - Page 138
By M. Rose-Innes (Yokohama)
Reconstruct the multiplication.
A B C D E
F G A
-------------
* * H * * *
B B * * *
* * H * * *
-----------------
* F * * * D * *
28) Sphinx - Sep 1933 #157 - Page 138
By C. A. Rupp (from American Mathematical Monthly)
ABCB, BCAD and CBAD are squares.
29) Sphinx - Sep 1933 #158 - Page 138
By C. A. Rupp (from American Mathematical Monthly)
ABCDE and BACED are squares; C + D and B + E are
consecutive primes. What are these numbers?
30) Sphinx - Sep 1933 - Page 141
By R. Man.
S E P T E M B R E S E P T E M B R E
- E R B M E T P E S + E R B M E T P E S
-------------------- --------------------
M P P B R P S S M B * R B M R R E B
31) Sphinx - Oct 1933 #162 - Page 155
By R. Man.
ABCABD = DEB2
32) Sphinx - Oct 1933 #163 - Page 155
By R. Man.
ABCD is divisible by 17.
CADB is divisible by 11.
CDBA is divisible by 7.
And all these three numbers are divisible by 3. What are they?
33) Sphinx - Oct 1933 #164 - Page 155
By R. Man.
The prime number AAAB, multiplied by 7, gives the product BEEDC.
The same number AAAB, multiplied by 11, gives the product ADDFB.
What is this number?
34) Sphinx - Oct 1933 #166 - Page 156
By M. Pigeolet (Anvers)
Find the key of this multiplication.
B O U L E
R A D I S
-------------
1 . . . . 0
1 1 . . . 0
1 0 1 . . 0
. . 0 . 0
. . . . 0
-------------------
. . . . . . . . .
35) Sphinx - Oct 1933 - Page 157
By R. Man.
OCTOBRE is divisible by 3 and by 7.
O
+ C T O
---------
B R E
36) Sphinx - Oct 1933 - Page 157
By M. Pigeolet (Anvers)
Reconstruct the multiplication:
* * * * * * where: O C T O
* * C T O
------------- C T O B
* * * * * * T O
* * * * * * T O B R
--------------- T O B R E
O C T O B R E O B R E
B R E
B R
R E
E
are 11 prime numbers.
37) Sphinx - Oct 1933 #21 - Page 159
By M. Pigeolet (Anvers)
Reconstruct the multiplication.
C * A A
R C C I K
-----------
A A C C K
* * * * *
* * * * *
* * * * *
* * * * *
-------------------
K R A I T C H I K
38) Sphinx - Nov 1933 #166 - Page 167
By M. Pigeolet (Anvers)
GALLUS and AMICUS are squares,
MAN and LANGE are primes,
UME and GEMIS each of them equals three times a prime number.
39) Sphinx - Nov 1933 #167 - Page 167
By M. Pigeolet (Anvers)
Reconstruct the multiplication.
T O C K
T O C K
----------
* * * * *
* * * * *
* * * * *
* * * * *
-----------------
* * * * T O C K
40) Sphinx - Nov 1933 #168a - Page 167
By M. Pigeolet (Anvers)
Reconstruct the extraction of square root.
* R * E
-----------------
\/ L A P I E R R E
*
-----
* * *
* * *
---------
* * * *
* * * *
-----------
* * * * *
* * * * *
---------
0
41) Sphinx - Nov 1933 #168b - Page 167
By M. Pigeolet (Anvers)
Reconstruct the extraction of square root.
* * P I
-----------------
\/ L A P I E R R E
*
-----
* * *
* * *
---------
* * * *
* * * *
-----------
* * * * *
* * * * *
---------
0
42) Sphinx - Nov 1933 - Page 170
By M. Pigeolet (Anvers)
Reconstruct the multiplication:
V E N T
N O V E M B R E
-----------------
N . . . E
M . . . R
O . . . B
S . . . M
N . . . E
E . . . V
R . . . O
B . . . N
-------------------------
. . . . . . . . . . . .
43) Sphinx - Dec 1933 #171 - Page 184
By M. Pigeolet (Anvers)
ABACDEBDECA is a cube,
AB, ACD and ECD are cubes,
EBD is a square.
44) Sphinx - Dec 1933 - Page 187
By M. Pigeolet (Anvers)
Reconstruct the extraction of square root.
* * * *
-----------------
\/ D E C E M B R E
* *
-----------
* * * * * * *
* * * * * * *
-----------
* * * * * * * * *
* * * * * * * * *
---------
0
45) Sphinx - Dec 1933 - Page 187
By M. Roses-Innes (Yokoama)
Reconstruct the multiplication and the square root extraction.
The multiplier A * * * O is the square of B * * ,
N O E L
A * * * O
-----------
* * * * *
* * * * *
* * * *
* * * *
* * * *
-------------------
\/ * * * * * * * * * | N * B * *
*
---------
* * *
* * *
---------
* * * * *
* * * * *
-------------
* * * * *
* * * * *
---------
0
46) Sphinx - Jan 1934 #2 - Page 11
By R. Man (Brussels)
Find the key: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 by the following factorizations:
P H A R E = P × I × P A × R A
D E L A I = S H × O E O A
A L O R S = H × S S × E S × O I
47) Sphinx - Jan 1934 #3 - Page 11
By A. Baudenne (Annevoie)
Reconstruct the multiplication and find the key-exhortation to
everybody's participation: 1 - 2'345674 - 1890.
V A L I S E
M O R U E
---------------
* * * 1 6 1 6
* * * * * * *
* * * * * * *
* * * * * * *
* * * 3 2 3 2
-----------------------
* * * * * 1 6 1 6 1 6
48) Sphinx - Jan 1934 #4 - Page 11
By Lapierre (Wattrelos)
Reconstruct the multiplication.
A B C D E
C E D B A
-----------
* * * * *
* * * * F
* * * * * G
* * * * * D
* * * * * A
---------------------
* * * * * * * * * *
49) Sphinx - Jan 1934 #5 - Page 11
By Rose-Innes (Yokohama)
All 3's are given.
* * 3 *
* * 3
---------
3 * * *
* * * 3 3
* * * *
----------------
* * * * * * *
50) Sphinx - Jan 1934 #6 - Page 11
By Paul Fayard (Decazeville)
Translate into words the following phrase: 7170 - 52 - 362840.
All 1's and 0's are given in the partial products and total product.
R I V E
F L A N C
-----------
* * * * 0
* * * * 0
1 * * * 0
* 0 * * 0
1 * * 1 0
-------------------
* 1 * * 0 * * * 0
51) Sphinx - Feb 1934 #7 - Page 24
By Gallus (France)
Two French mathematicians have 8 letter-sized names which,
transformed into figures by means of the key 12-34567890, give
two numbers from which the square roots are extracted.
Herein, below, you'll find what we know about the two operations,
where the letters must be replaced with the corresponding figures.
The key is, in the broad sense, the birthplace of one of the
mathematicians, but not of the other one.
As for their death, it occurred in the century that is the maximum
common divisor of the two names.
O I A O O C . .
----------------- -----------------
\/ . . . . . . . . \/ . . . . . . . .
. . . .
------- -------
. . . L E . .
. . C . . .
--------- ---------
. C . . . . . .
. . . . . . . .
----------- -----------
. . . . . . . . . .
O . . A O . P . . .
--------- ---------
. . . O . . . V
52) Sphinx - Feb 1934 #8 - Page 25
By Colaço (Castro-Verde)
What is the key for these two operations?
L I O N
R A T
-------------
L T H L R T
O P H P L
----------------
L A P I N | O A H N R R T | R N
O P N I E L
-------------
E L T L L T
E E E T R H
-----------
E L P L
53) Sphinx - Feb 1934 #9 - Page 25
By S. Vatriquant (Brussels)
* * * * R E L U E = ( L U E )3
54) Sphinx - Feb 1934 #10a - Page 25
By M. Pigeolet (Anvers)
The numbers 90ABC17, 79ABC and 491ABC4 are not relative prime.
What are these numbers?
55) Sphinx - Feb 1934 #10b - Page 25
By M. Pigeolet (Anvers)
The numbers ABCD, 1920CD41, 496BC3, 872AB76 and 10A25D8
are not primes. What are these numbers?
56) Sphinx - Feb 1934 #10c - Page 25
By M. Pigeolet (Anvers)
COLAÇO is a square and - CO + LA = ÇO.
There are two solutions; don't consider the cedilla under
the second C.
57) Sphinx - Feb 1934 #11 - Page 25
By Rose-Innes (Yokohama)
ABC × BCA × CAB = D63106938 if A > B > C
58) Sphinx - Mar 1934 #13 - Page 39
By K. de Haan (Velsen, Holland)
The sums of the numbers in the multiplier and in the
multiplicand are equal.
. . . . . . .
. . . . . . . .
-----------------
. . . . . . . Q
T . . . . . . U
I . . . . . . E
O . . . . . . S
S . . . . . . T
E . . . . . . I
U . . . . . . O
Q U E S T I O N
-------------------------------
. . . . . . . . . . . . . . .
59) Sphinx - Mar 1934 #14 - Page 39
By Amicus (Brussels)
Willing to break off from a (female) creature with an acid character, a chemist
left the following note for her:
L I S O N = H2 S O4
However, this note made the darling creature smile, as her name, which was
so little gallantly factorized, was also equivalent to the amount of the cheque
joined to the note. How much is the price of the break-off ?
60) Sphinx - Mar 1934 #15 - Page 39
By A. Rose-Innes (Yokohama)
ABC × ACB × BAC × BCA × CAB × CBA = 298316E551967600
if A = 2 ( E - C )
61) Sphinx - Apr 1934 #16 - Page 60
By Gallus (Lambres)
Waiter! The bill, please...
A group of friends entered a pastry shop whose mark represents an animal
that covets a saucer: "83 5681 734 023569".
Each person took a cup of their favourite drink (four different drinks: the first
4 lines of the bill), plus one pastry, the same order for everybody (the 5th line).
Finally, the waiter (a cryptarithm buff), brings the bill. The names of the
consumed items, pre-printed in the small note, are in the singular. The digits
replace the letters and reciprocally.
Reconstruct the mark, the bill, the political opinion of the shop owner:
5816204739, and the author's name: "527", from Lambres, in Pas-de-Calais.
Unit
Quantity Item Price Amount
-----------------------------------------------
C 0841 U.QC TA.QC
E 169 U.OC OE.OC
A 58582 8 0'983 O.-- TH.--
C 56252081 I.-- OL.--
OQ 523739 T.IL UQ.AL
----------------------------------------------
TOT.AL
62) Sphinx - Apr 1934 #17 - Page 60
By A. Decerf (Paris)
The snore sound number RABOUBOUMRAM is divisible by
2B5200B49.
You will find this number by knowing the rules of divisibility by E, by UL
and by UU, etc. and practising the imperial Latin motto: 386097214.
63) Sphinx - Apr 1934 #18 - Page 60
By G. Cottin (Brussels)
(LAVALSEDAN)2 = * * * * * * * * * * LAVALSEDAN and
(SEDAN)2 = LAVALSEDAN.
64) Sphinx - Apr 1934 #19 - Page 60
By G. Fistié (Maestricht)
Reconstruct these two connected multiplications. One is to be read normally
but the other requires a half turn of the leaf.
* * * * * * * *
-----------------
* * * * *
* * * * *
* * * *
* * * *
---------
H S I X
O I Z H
---------
* * * X
* * * * *
* * * X
* * * *
-----------------
* * * * * * * *
65) Sphinx - Apr 1934 #20 - Page 61
By M. Legros (Jodoigne)
A big blot of ink spilled over a multiplication permits identifying only
its multiplicand 1234 and some digits of the product 4***38.
Reconstruct the multiplication.
66) Sphinx - May 1934 #21a - Page 71
By M. Pigeolet (Anvers)
Reconstruct the multiplication.
S P H I N X
* * * * * * *
---------------
S P H I N X
X S P H I N
N X S P H I
I N X S P H
H I N X S P
P H I N X S
S P H I N X
-------------------------
S * * P * H I * * N * X
67) Sphinx - May 1934 #21b - Page 71
By M. Pigeolet (Anvers)
Reconstruct the multiplication.
P O S I T I F
N E G A T I F
-----------------
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * * *
* * * * * * *
-----------------------------
N * * * * * * * E G A T I F
68) Sphinx - May 1934 #22 - Page 71
By Raphaël Robinson (Berkeley, USA)
Instead of a product of two powers: ab . cd a printer, accidentally,
composed this 4-digit number: abcd. However, the value is the same.
Find this unique number.
69) Sphinx - Jun 1934 #24 - Page 91
By A. Lapierre (Mouscron)
After the sudden death of a wise astronomer, a piece of semi-burnt paper was
found in his fireplace where we can identify the remains of the arithmetical
operation shown below. Can our Oedipuses reconstruct this document?
A * *
------------------
* * * * * *
*
--------
* * * * * *
* * * A *
---------- *
* * * * * ----- * *
* * * * * * *
-------- *
----
* A
70) Sphinx - Jun 1934 #25 - Page 92
By A. F. Colaço (Castro-Verde)
The numbers:
TSRABVOLUE, RSBAOVTULE, OSBURVLETA,
UBOSLRVEAT, VLSOAEBTRU, AUBTOELSRV,
BEOVSALRUT, LTOVABERSU, ELTUSBROVA,
are squares. What is the key?
71) Sphinx - Jun 1934 #26 - Page 92
By R. Man (Brussels)
A well known French name is the key of this multiplication,
to be solved to the base 8 system.
L O T I
R A V I
-----------
* * * * T
L * * *
* * * * I
O * * * *
-----------------
L * * * E * O T
72) Sphinx - Jun 1934 #27 - Page 92
By C. Miliopoulo (Fontainebleau)
The fragment of a cryptarithmetic table of squares and cubes was found.
You are required to reconstruct the table.
* D * * * * * * * * * * * * * * D A
* * * * * * * * * * * * * * * * D *
* * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * *
* * B * * B * * C * * * * * * * * B
73) Sphinx - Jun 1934 #28 - Page 92
By M. Legros (Jodoigne)
The sum of the digits represented by the letters in the following
words form up an ascending arithmetical progression.
POIRE, OPERA, PORTE, TAPIS, ASTRE, PATRE, LOTUS,
LISTE, LOUPE, OUTRE, . . .
74) Sphinx - Jun 1934 #29 - Page 92
By G. Fistié (Maestricht)
S E L L E S is a square.
75) Sphinx - Jul 1934 #33 - Page 102
By M. Legros (Jodoigne)
Reconstruct the following dance where each letter
stands for a prime number.
V A L S E
S L A V E
-------------
* * * * * *
* * * * * *
* * * * * *
* * * * *
* * * * *
-------------------
* * * * * * * L E
76) Sphinx - Jul 1934 #34 - Page 102
By G. Fistié (Maestricht)
Knowing that DEF and FAE are multiples of 11 and that
D E F
F A E
* H F
---------
* * H D
find the number D***A***F which is a cube.
77) Sphinx - Sep 1934 #36 - Page 136
By A. Baudenne (Annevoie)
ADELE, the farmer, reversed her grog inadvertently:
L E G R O G D E L A F E R M I E R E
+ E R E I M R E F A L E D G O R G E L
-----------------------------------------------
3 * * 1 4 * * 1 5 * * * * * * 9 * *
She asks her husband ROGER to reconstruct her grog knowing that
A D E L E
+ R O G E R
------------
9 8 9 3 7
ROGER is completely... groggy!
But that doesn't prevent him from continuing to read
"12 3456472 82 967450"
78) Sphinx - Sep 1934 #37 - Page 136
By G. Cottin (Brussels)
OHEM and OMLI are the squares of two consecutive numbers: RG and
RA, respectively.
Also RG + RA = LET, and OHEM + OMLI = RTOR.
What is the key?
79) Sphinx - Sep 1934 #38 - Page 136
By M. Pigeolet (Anvers)
Reconstruct the multiplication.
X S P H I
* * * * *
-------------
S P H I N X
X S P H I
I N X S P H
H I N X S P
---------------------
* S * * * S S S * *
80) Sphinx - Sep 1934 #39 - Page 136
By A. Colaço (Castro-Verde)
GALON and ALONG are the squares of GOO and OOG respectively
to the base 6 system. What are these numbers?
81) Sphinx - Sep 1934 #40 - Page 136
By C. Milopoulo (Fontainebleau)
When the numbers 1234567890 are substituted for an
English word, it is possible to make the following magic
square. The sums of the rows, columns and diagonals
are 275.
R L A A C N B D R C
A E M C M L E A R B
U A M B E E L R A U
B R E U L M L N U E
B N L D N C U U B M
82) Sphinx - Oct 1934 #41 - Page 149
By G. Cottin (Brussels)
Find the key, knowing that R is a prime:
A L G E R = R2 × N I G
D E L T A = R [(A A D R x O) + R]
83) Sphinx - Oct 1934 #42 - Page 149
By A. F. Colaço (Castro-Verde)
In the system of numeration base 6, we have:
A M I C U S is a square,
A is a square,
M I is to the fifth power,
I C U S is a square,
U S is a square.
84) Sphinx - Oct 1934 #43 - Page 149
By G. Fistié (Maestricht)
Find PIGEOLET, which is a cube. All the T's are given.
E * * * T
* * E T
-------------
* * * * E T
T * * * *
E * * * * *
E * * * T
-----------------
P I G E O L E T
85) Sphinx - Nov 1934 #47 - Page 169
By G. Fistié (Maestricht)
A A A U2 = A L U M I N E if:
(A + A + A + U)2 = A + L + U + M + I + N + E.
86) Sphinx - Nov 1934 #48 - Page 169
From: The Strand Magazine (1922)
Reconstruct the multiplication:
N X P S I × H = S P H I N X
87) Sphinx - Nov 1934 #49 - Page 169
By A. Rose-Innès (Yokohama)
There are eight brothers and sisters in a family: Georgette, Ulysse,
Yvan, Marie, Annette, Roger, Isidore and Emile. All are less then
10 years old. If you represent the age of each child by the first
letter of its name, you obtain:
Y U
------------
G U Y | M A R I E
M A R E
---------
E E
If Marie is the youngest of the sisters, what is her age?
88) Sphinx - Dec 1934 #52 - Page 185
From: Denksport 1933 (Amsterdam)
All the digits and zero are used in the multiplier and the
multiplicand. All the 2's in the problem are given. Find
the two solutions.
* * * * *
* * 2 * *
-------------
* * * * 2 *
* 2 * * 2 *
* * * 2 * *
* * * * 2 *
2 * * * * 2
---------------------
a): * 2 * 2 2 * * * * *
b): * 2 * * * * * * * *
89) Sphinx - Dec 1934 #54 - Page 185
By A. Gloden (Luxemburg)
A B B C C A is a square, in which C = 2B.
90) Sphinx - Dec 1934 #55 - Page 185
By R. Baras (Saint-Cloud)
The series of numbers:
NC - NL - NO - NU - TD - TS - TA
forms an ascending arithmetic progression and the sum of these
numbers is: I N I. What is the key?
91) Sphinx - Dec 1934 #56 - Page 185
By G. Cottin (Brussels)
Find the key of this pair that must be solved together:
C H I N E C H I N E
+ I N D E - I N D E
----------- -----------
H O E E C C O P R Y
92) Sphinx - Dec 1934 #57 - Page 185
By A. Baudenne (Annevoie)
An extract from a historical novel: "Facing this terrible sight, the duchess
uttered a terrifying cry: HARRY, CAYLUS SE TUE ...!!! " (Harry, Caylus is
killing himself...!!!); and the echo quickly repeats it by the thousand.
A R R Y C A Y L U S S E T U E
U T L A
----------------------------------
Y L U S S E T U E H A R R Y C A
A Y L U S S E T U E H A R R Y C
C A Y L U S S E T U E H A R R Y
Y C A Y L U S S E T U E H A R R
---------------------------------------
Y E T S E T U E H A R R Y C A Y T T A
|
1) 462193 x 3952617 = 1826871909081
2) 625=54, 256=44
3) 567 = 3 × 189
4) 4913-3375-5832-2744-4096-6859-9261-1331-1728-8000
5) 18671041 = 43212
6) 234 = 3 × 78
7) 682276 ÷ 826 = 826
8) 4502652 ÷ 28 = 160809
9) x=8, y=9, z=10
ABC=271, ACB=217, ABC+ACB=488
10) 994009 = 9972
11) 4213 × 2486 = 10473518
12) 715716 = 8462
13) 1 2 3 4 5 6 7 8 9 0
N P S A I M E L R O
14) 15460632 ÷ 95436 = 162
15) 20449 = 1432
16) 168 × 30275 = 5086200 ÷ 49 = 103800
17) 341737 × 576 = 196840512
18) PIGEOLET = 08163265
19) ROSE-INNES = 9216-53361
20) 969 × 199 = 192831
21) The problem admits 3 solutions. Dividend=18530
or 18531 or 18532. Divisor=627. Quotient=29.
22) 7932 = 628849
23) NED=925, SASH=1813, SHUN=1369, SEND=1295, SEED=1225.
24) 10162 = 1032256
25) 5552 = 308025
26) 3527 + 3735 = 7262, 7253 - 2177 = 5076
27) 49607 × 524 = 25994068
28) ABCD=1296, BCAD=2916 and CBAD=9216.
29) ABCDE = 18769, BACED = 81796
30) SEPTEMBRE = 721425902
31) 183184 = 4282
32) ABCD=9741 or ABCD=9027
33) AAAB = 2221
34) 14530 × 62789 = 912324170
35) OCTOBRE = 7197204
36) 112979 x 87 = 9829173
37) 6733 × 86625 = 583246125
38) 1 2 3 4 5 6 7 8 9 0
N A E U M G I L S C
39) 9376 × 9376 = 87909376
40) 10465225 = 32352
41) 15984004 = 39982
42) 9871 × 75983648 = 750034589408
43) ABACDEBDECA = 27216576512 = 30083
44) 16760836 = 40942
45) 1936 × 54289 = 105103504 = 102522
46) 1 2 3 4 5 6 7 8 9 0
S P H E R O I D A L
47) 612904 × 83754 = 51333161616
1-2'345674-1890 = A-L'OEUVRE-AMIS
48) 24697 × 67942 = 1677963574
49) 1237 × 893 = 1104641
50) 6170 × 35284 = 217702280
7170-52-362840 = VIVE-LA-FRANCE
51) 1 2 3 4 5 6 7 8 9 0
L A P R O V I N C E
57252 = 32781060 = PAINLEVÉ
59822 = 35789240 = POINCARÉ
XXth century
52) 1 2 3 4 5 6 7 8 9 0
O R P H E L I N A T
53) 420189749 = 7493
54) ABC=315 or ABC=862
55) ABCD=8524
56) COLACO=163216 or COLACO=367236
57) 943 x 439 x 394 = 163106938
58) 9188837 × 75436928 = 693177635172736
59) 61250 = 72 . 2 . 54
60) 651 × 615 × 561 × 516 × 165 × 156 = 2983164551967600
61) mark: AU CHAT QUI LOUCHE
owner's political opinion: CATHOLIQUE
author's name: COQ
62) RABOUBOUMRAM=986016012982, 386097214=LABOREMUS
63) (8212890625)2 = 67451572418212890625
(906252 = 8212890625
64) 1368 × 7691 = 10521288
1967 × 8631 = 16977177
65) 1234 × 357 = 440538
66) 142857 x 1326451 = 189492810507
67) 7842625 x 1390625 = 10906150390625
68) 25 × 92 = 2592
69) 932574833 = 9773
70) 1 2 3 4 5 6 7 8 9 0
T R O U V A B L E S
71) 1 2 3 4 5 6 7 0
V O L T A I R E
72) 475 - 476 - 477 - 478 - 479
73) 1 2 3 4 5 6 7 8 9 0
S P O L I A T E U R
74) 698896 = 8362
75) 37215 × 12735 = 473933025
76) DEF=517, FAE=781, D***A***F=517781627
77) 1 2 3 4 5 6 7 8 9 0
L E M A R I G D F O
78) 1 2 3 4 5 6 7 8 9 0
L O G A R I T H M E
79) 76923 × 34109 = 2623766607
80) 15324 = 1222, 53241 = 2212 to the base 6
81) 1 2 3 4 5 6 7 8 9 0
C U M B E R L A N D
82) 1 2 3 4 5 6 7 8 9 0
A N G L E D R O I T
83) AMICUS = 452013 to the base 6
84) 26645 x 1825 = 48627125
85) 11132 = 1238769
86) 54618 × 3 = 163854
87) Three years old. The key is: 1 2 3 4 5 6 7 8 9 0
E I M G A R Y U
88) a) 89104 × 36275 = 3232247600
b) 65103 × 49287 = 3208731561
89) 7152 = 511225
90) 1 2 3 4 5 6 7 8 9 0
S A I N T C L O U D
91) 1 2 3 4 5 6 7 8 9 0
P O N D I C H E R Y
92) 1 2 3 4 5 6 7 8 9 0
S Y C U A T E R L H
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Last updated: September 1st, 2010.
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