there are only 2 solutions: 78981/101547 and
79191/101817.-michael marfil
I think your puzzle has the solution…
SEVEN = 78981
NINTHS = 101547
Also, see http://users.aol.com/s6sj7gt/mikealp.htm for
Mike Keith's alphametics page – taking them to the
extreme. There are some truly (perhaps maximally) dense
puzzles there.
Regards
Mark Michell
The first double true of this kind I know was
by Jesus Sanz and was send to the spanish puzzle
list Snark some monthes ago, maybe more, was:
Cripto Fraccion 1: (Jesus Sanz)
TRES/OCHO = 3/8
Then I found:
Cripto Fraccion 2:
TRES/NUEVE = 3/9 sin usar el 0.
4562/13686
Cripto Fraccion 3:
CUATRO/VEINTE = 4/20
170469/852345
Cripto Fraccion 4:
CINCO/TRECE = 5/13
30435/79131
Cripto Fraccion 5:
SEIS/DIEZ = 6/10
4914/8190
Cripto Fraccion 6:
SEIS/TRECE = 6/13
6876/14898
Cripto Fraccion 7:
SIETE/TRECE = 7/13
17535/32565
Cripto Fraccion 8:
DIEZ/TRECE = 10/13
9650/12545
Cripto Fraccion 9:
(UNO+SIETE)/CINCO = 8/5
670+54898/34730
Cripto Fraccion 10:
(DOS+NUEVE)/CINCO = 11/5
357+64818/29625
Cripto Fraccion 11:
(TRES+TRECE)/CINCO = 16/5
8473+84727/29125
Cripto Fraccion 12:
(SEIS+QUINCE)/CINCO = 21/5
9389+278563/68560
I also found this kind of problem/solution in English
but I cannot find now.
My daughter has 1 and 1/2 year, no time for puzzles!
Best wishes,
Rodolfo Kurchan
Dear Sir,
E = 8, H = 4, I = 0, N = 1, S = 7, T = 5, V = 9
SEVEN = 78981
NINTHS = 101547
SEVEN/NINTHS = 78981/101547 = 7/9
Regards,
Veo Chau
Seven 78981
Ninths 101547
Neil Jones
Bryce problem
7/9 = 78981/101547.
Regards
Eswaran Narasimhan
Hi Ed,
I solved Bryce Herdt's proportion:
SEVEN/NINTHS=7/9
78981/101547=7/9 or {S=7, E=8, V=9, N=1, I=0, T=5, H=4}
Solution strategy (since I like to see people's methods):
(1) 7x < 100,000 and 9x >= 100,000 (given number of letters)
(2) 11,111 < x < 14,285 (from 1)
(3) N=1 (since 9x < 128,565 from 2)
(4) 11,248 < x < 13,555 (since 101,234 < 9x < 121,987 from 3)
(5) S=7 (since 7x ends in 1 --> x ends in 3 --> 9x ends in 7)
(6) 78,736 < 7x < 79,996 (from 4,5)
(7) 78,771 < 7x < 79,961 (from 3,6)
(8) SEVEN = 78,981 or SEVEN = 79,891 (by scrolling through all
seventeen possible cases of 78,771 + 70n < 79,961 on a
calculator and noting the two cases where E=E)
(9)SEVEN = 78,981 (since 79,891*(9/7)=102,717 NINTHS)
and NINTHS = 101,547
- Matt Sheppeck
This is my solution to the SEVEN/NINTHS problem
by Michael Trigiani
I did this problem by hand with some trial and error.
7x = SEVEN and 9x = NINTHS
I found the lower and upper bound for x. The upper bound is found by
98784/7 = 14112 (98784 is the highest possible number SEVEN could be
divisible by 7). The lower bound is found by 101259/9 = 11251 (101259 is
the smallest possible number NINTHS could be divisible by 9). Therefore the
range that x could be is 11251-14112.
14112*9 would give the range that NINTHS could be, which is 127008. This
tells us that N=1, which also tells us that the ones digit in x is 3, and
also tells us that S=7
7x = 7EVE1 and 9x = 1I1TH7
I know found a new upper and lower bound for x. The upper bound is found by
79891/7 = 11413 (79891 is the highest possible number SEVEN could be
divisible by 7). The lower bound is found by 70301/7 = 10043 (70301 is the
smallest possible number SEVEN could be divisible by 7). Therefore the
range that x could be is 10043-11413.
11413*9=102717 which shows that I=0.
7x = 7EVE1 and 9x = 101TH7
Because 1+0+1+7=9, then the sum of T+H must be a multiple of 9. The only
possible choices for NINTHS at this point would be (101367, 101457, 101547,
101637). Dividing each of these choices by 9 would in the possibilities of
what x is. (101367/9=11263, 101457/9=11273, 101547/9=11283, 10163/9=11293).
Using these possibilities for x and multiplying them with 7 will determine
the value of SEVEN (11263*7=78841, 11273*7=78911, 11283*7=78981,
11293*7=79051).
SEVEN=78981, NINTHS=101547, SEVEN/NINTHS=78981/101547=7/9
seven/ninths = 78981/101547
Jeff Smith
Hi Ed,
78981/101547 fits the bill.
Regards,
Mike Shafer