A O U T T U O A
+ A T A O - U * T T
---------- ----------
T U * U O * T *
Can you solve these addition and subtraction problems, knowing that AOUT as well as it's reverse TUOA is a prime number?
TUOA prime means A is odd and not 5. A=7 or A=9 makes the addition result five digits long so (A,T) can only be (1,3) or (3,7).
Say (A,T)=(1,3). From the subtraction A-T requires a 'borrow' so O=8. Back to the addition, T+O makes U=1, impossible since A=1.
So we have (A,T)=(3,7). As above O=5, T+O makes U=2, and AOUT=3527. Checking, that's a prime as is its reverse.
The completed sum is 3527+3735=7262. There's a dual solution for the difference, 7253-2077=5176 and 7253-2177=5076.
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Posted by xdog
on 2024-01-19 19:43:07 |
solution
