Here is the link to the YouTube video by MindYourDecisions:
Puzzle From A Math Teacher - If AAA + BBB + CCC = BAAC, What Are A, B, C = ?
The solution seemed a bit too complicated to me. My take which I think is a bit easier...
AAA
BBB
CCC
CCC
----
BAAC
1. Given base 10, looking at the digits column, A+B=10 (2 digits cannot add to 20)
2. Since we carry a 1 to the 10s column, C+1=A (Cannot carry a 2, see above)
3. Since, A+B+C results in carrying a 1, looking at the thousands column, B=1.
Putting B=1 into 1. above gives A=9 (from A+1=10)
Putting B=1 into 1. above gives A=9 (from A+1=10)
Putting A=9 into 2. above gives C=8 (from C+1=9)
We now have A=9,B=1,C=8 or:
We now have A=9,B=1,C=8 or:
999
111
888
888
----
1998
Is there a flaw in this reasoning chain?
Consider this wrinkle:
Consider this wrinkle:
BCA
CAB
ABC
ABC
----
BAAC
Indeed, order that has one and only one of A,B, and C in a column will give the same sum BAAC.
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