# Why Does 3762 + 8271 Equal What It Does?

• bblueblob
In summary, the math problem has a base of nine, and adding two numbers with different bases results in a larger sum than the base ten sum.
bblueblob
Can anyone help me figure out this very hard math puzzle?

2 + 2 = 4
4 + 4 = 8
142 + 468 = 621
3762 + 8271 = ?

PS. It is very confusing!

bblueblob said:
Can anyone help me figure out this very hard math puzzle?

2 + 2 = 4
4 + 4 = 8
142 + 468 = 621
3762 + 8271 = ?

PS. It is very confusing!
It shouldn't be! The only way the first three lines can be true is that the base is not ten. But it has to be very close to ten as the third line is very close to the correct addition for base ten: i.e., in base ten, 142+468=610. Since the result obtained above is larger then the base ten result, the base for the problem must be less than ten. Secondly, the base must be odd! Note that the third line has even numbers in the units place and the sum is odd in the units place therefore the change in parity of the units place must come from the higher entries.

Your best bet is a base of nine. Check it out and it works fine. Do the third line. Two plus eight is ten; in base nine that means one and carry one. The second place is four plus six plus the carry is eleven; in base nine that means two and carry one. Finally, one plus four plus the carry is six. So the answer in base nine is 621.

The fourth line is given by two plus one is three; six plus seven is thirteen (in base nine that's four and carry one); seven plus two plus the carry is ten (in base nine that's one and carry one); finally three plus eight plus the carry is twelve (in base nine that's three plus a carry). Clearly, in base nine, 3762 + 8271 = 13143.

It's a cute problem -- Dick

Thank You very much! undefined

oh wow didnt even see this thread.. i am confused on the bases though.. how do you add with a different base? i know you wrote it above but ihave no idea why you are counting like that.

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