In this multiplication problem, the 5 characters shown above represent 5 different numbers. Can you figure out what number corresponds to each character? There is no zero.
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4973 x 8 = 39784
4973
x 8
——
39784
I had to use the old “plug and chug” method to get it, though…
4 = lady with earrings
9 = nutty professor
7 = hippy chick
3 = doc holliday
8 = mork’s uncle
4,973 x 8 = 39,784
4973 x 8 = 39784
I think the answer is:
4973
X..3
39784
cool puzzle, I think it was key to find out the possible values of A that were very little and from that on, trial and error for me.
4973 x 8 = 39784
Thanks 4 this puzzle site! MATH RULES! Cool site, really. thanks again. Keep ‘em coming, please!
Clearly, the 2 #’s in 1′s position couldn’t be 0, 1, or 5, and neither could be 6 if the other was an even #. And there were a few other general rules that became clear and allowed me to eliminate a lot of potential nos initially. But I eventually had to resort to trying potential combos of the 2 no’s in right-most position. I would have liked to come up with a system of equations to solve this — as I believe I ought to be able to do– rather than the ‘try to plug in possible solutions’ method. Any helpful hints on the most efficient methodology?
thx. Chris
4973 times 8 = 39784. I’ve never used this site b/f 2day, so I’m checking 2 see whether the no of comments increases when I tell the system to post this response. Sorry 4 the redundancy, and thanks again for the cool site. Chris.
Hey there Chris, thanks for visiting and liking the site
As you describe, there are a few general rules that constrain some of the #’s, but I think there’s some plug & chug that’s necessary. However, am curious to see what Hex, Bobo, Shawn,Suineg etc… have to say
@Shawn LOLs Mork’s uncle!
Used to watch that show too
it was 8 in my comment as you see because 3×3 would be 9…, too much sleep disorder I guess.
@Chris Edwards: In this one I did not find any kind of equation system that helped me solved this problem right away, however, for me what really was helpful was translate this problem to a letter problem like this:
..ABCD
..X..E
=DBCEA
From this , for me what really reduce the search were the possible values of A
First A,B,C,D,E are differents numbers so:
A cannot be 1, because the only number that can be formed like that with 2 different digits is DXE=21 where D should be 7 or 3, but if A is 1, the maximun possible value of D would have been 1
A cannot be 3,5, the numbers are differents so it is impossible.
A cannot be 9 or 7, in the case of 9 because there is no multiplication between 2 different digits that gives you that unit digit, in the case of 7 , the only case is 9X3=27, D cannot be 9 for the reason exposed before so you assume E is 9, but EXA would be 63 so it gives you an incongruency with D
so A can be 2,4,6,8 with similar reasonings you get that the only possible value is 8 from that on it became very easy to find the others values.
its 4 I meant, then you deduce the value of E and D and the rest is easy peasy
@ Suineg : thanks for your response. Interesting how we approach things from different angles!
I, too, used the same naming convention; ie, ABCD X E. But I focused on the possible values of D and E, noting that, of course, neither could be 0 nor 1, nor 5 because A would result in either a zero or another 5. Also, if either D or E is a 6 and the other is an even number, then A would be that same even number. And if E is even, the carry can’t be odd because E must be even, nor can c=1. I had been up too many hours before I started ‘playing’ with this puzzle to do my best reasoning. Next time, I’ll have to try it rested!
Thanks again 4 yer response!
Chris
@ RK : Thank you 4 the welcome and for your response . And thx 4 the site!
Confession time. I wrote a quick program on my TI-84 to run through all the possibilities.
I started to look for conditions/equations which would help narrow the selection choices. However, being short of time, I quickly derived the resulting condition and threw up a small Pascal program that did the job in less than 1 second:
for a:= 1 to 9 do
for b:= 1 to 9 do
for c:= 1 to 9 do
for d:= 1 to 9 do
for e:= 1 to 9 do
if 10000*d + 1000*(b-a*e) + 100*(c-b*e) + 10*(e-c*e) + (a-d*e) = 0 then
writeln(a,b,c,d,e);
Hahaha! I love computer and math peeps. My initial reaction was that it kind of ruins the point of doing a puzzle by having the computer find the solution 4 U, but writing a program is certainly the most efficient approach! And programming is fun! R U writing programs 4 the sake of your ‘stats’ or b/c when U C a math problem U must find the solution? I’m of the latter persuasion… Thanks 4 the input!