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A four digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?
Answer
The only number is 2592. 2^5 is 32 and 9^2 is 81. 32*81 is 2592.Hide Answer Show Answer
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Comments
Any number represented by ABCD means that A, B, C & D are all different digits. But the according to the answer, A is equal to D.
In that case, ABCD should instead be ABCA or DBCD.
In that case, ABCD should instead be ABCA or DBCD.
That was very hard and a very good math question
I agree with V_Bapat you should say that A and D will be the same or change it to ABCA or DBCD or give some indication that they can be the same. I naturally assumed that they would all be different but it was still a really fun and challenging puzzle.
I got it! But it was a lucky guess. I thought it was an interesting problem. Thanks!
Anybody know how to approach this problem? I'm stumped!
I liked this one, it was very hard for me. I had to ask about and get help. Nice Job, and good teaser.
(I'm not that great in math )
(I'm not that great in math )
Just because the number is indicated as ABCD, doesn't necessarily mean that they are all different numbers. In this case it happens to be that A=D.
It took me less than 2 minutes and 15 lines of C code to do it. It's fun, but should be listed as a computer problem not math
Well, Snaps, generally, it is to be assumed that they are distinct digits, otherwise the same letters would be used, though I did curiously note the absence of the line claiming them all distinct, but thought nothing of it. As for Nomad - many of these math problems can be programmed and gotten, the real test is if you can do it actually, not with clever code (though I will nto say that is a completely invalid way to do it, you still need to code it properly, so kudos for that), but to figure it out mentally or with just a simple calculator is, I believe, it's intended purpose and aim. Would be interested to see any reasoining, though I think it's jsut guess and check.
can you tell how to find the number ??
is it gussing and finding all possible combinations or what ??
i did this eqn but cant solve it
1000A+100B+10D+C = A^B*C^D
is it gussing and finding all possible combinations or what ??
i did this eqn but cant solve it
1000A+100B+10D+C = A^B*C^D
In a complete fluke, I found this on the third number I tried. Just dumb luck with a little bit of thought to try 2^5. It's an interesting bit of trivia, but I don't know of any way to do this mathematically.
5 python lines;
for a in range(10):
for b in range(10):
for c in range(10):
for d in range (10):
if ((1000*a + 100*b + 10*c + d) == (a**b) * (c**d)):
print (1000*a + 100*b + 10*c + d)
for a in range(10):
for b in range(10):
for c in range(10):
for d in range (10):
if ((1000*a + 100*b + 10*c + d) == (a**b) * (c**d)):
print (1000*a + 100*b + 10*c + d)
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