For some Maniacal reason they gave this math problem to 9 year olds. Can you solve it?

JLW

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They do not use the American Alphabet in Taiwan so yeah, that would be tough. And most likely total B.S.
 
They do not use the American Alphabet in Taiwan so yeah, that would be tough. And most likely total B.S.
No there is a real solution.
 


No calculator. I think "for extra credit" was likely left out of the description.
 
Okay:


1) Neither A or E can equal 0.
2) A does not equal 1 (else (A * ABCDE) = ABCDE, not EEEEEE)
3) E does not equal 1 (else, A * ABCDE would yield A as the last digit of the result, not E)
4) A does not equal 2 (else (A * ABCDE) would be a 5-digit number, not 6 digits; 2 * 29,999 = 59,998)

Ruling out more digits for E:

5) If E=2, then A MUST equal 6 (to get (A * ABCDE) = EEEEEE). However, contradiction shows this permutation is not possible, as (222,222 / 6) yields 37,037. So, A would equal both 6 and 3. So, E does not equal 2.
6) If E=3, then A MUST equal 1 to get (A * ABCDE = EEEEEE). However, A cannot equal 1. So, E does not equal 3.
7) If E=4, then A MUST equal 6 to get (A * ABCDE = EEEEEE). However, (444,444 / 6) = 74,074. So, E does not equal 4.
9) If E=5, then A MUST equal one of: 3, 7, 9 to get (A * ABCDE = EEEEEE)
a) 555,555 / 3 = 185,185, so A does not equal 3, when E = 5
b) 555,555 / 7 = 79,365..... ding ding ding ding ding, there is ONE answer!

A=7
B=9
C=3
D=6
E=5


So there is ONE answer, reasoned out in the fewest possible steps without need of a calculator.

Now, what I have not shown is that this is the ONLY answer. This would take more work then what has been done already. So, in reality, nobody in this thread has actually solved the problem yet.
 
Last edited:
Completing the solution (to show there is a unique answer):

1) If (E,A) = (5,9): 555,555 / 9 = 61,728.3... So, A cannot equal 9, when E=5. So, when E = 5, A = 7.

2) If E = 6, A MUST equal 6 to get (A * ABCDE) = EEEEEE. However, this contradicts the rules. So, E cannot equal 6.

3) If E = 7, A MUST equal 1 to get (A * ABCDE) = EEEEEE. However, we know A cannot equal 1. So, E cannot equal 7.

4) If E = 8, A MUST equal 6 to get (A * ABCDE) = EEEEEE. However, 888,888 / 6 = 148,148. So, E cannot equal 8.

5) If E = 9, A MUST equal 1 to get (A * ABCDE) = EEEEEE. However, we know A cannot equal 1. So, E cannot equal 9.

Therefore, E = 5.

Therefore, A = 7, and, by 555,555 / 7 = 79,365,

B=9
C=3
D=6

NOW the problem has been solved.
 
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