BAMO 2011 Problem 2

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westin

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Hi,

Need help. Attached is BAMO ( Bay Area Math Olympiad) 2011 Problem 2. I don't know why the answer is 45.

I understand that first number has to be single digit. However, I think below examples also fulfil the requirement that the sum of the digits of the neighbor(s) of a given circle is equal to the number labeling that point.

3 -> 10 ->7 -> 15 -> 8 sum = 44
4 -> 10 -> 6 -> 14-> 8 sum = 42
7 -> 10 -> 3 -> 11 -> 8 sum = 39

also, the question did not mention that positive integers cannot be repetitive. in that case. there are even smaller sum value like below
8 -> 10 -> 2 -> 10 -> 8 sum= 38

however, attached is the official solution from the BAMO website. Can someone help and explain what is wrong in my thought process.

Thanks
 

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westin said:
Hi,

Need help. Attached is BAMO ( Bay Area Math Olympiad) 2011 Problem 2. I don't know why the answer is 45.

I understand that first number has to be single digit. However, I think below examples also fulfil the requirement that the sum of the digits of the neighbor(s) of a given circle is equal to the number labeling that point.

3 -> 10 ->7 -> 15 -> 8 sum = 44
4 -> 10 -> 6 -> 14-> 8 sum = 42
7 -> 10 -> 3 -> 11 -> 8 sum = 39

also, the question did not mention that positive integers cannot be repetitive. in that case. there are even smaller sum value like below
8 -> 10 -> 2 -> 10 -> 8 sum= 38

however, attached is the official solution from the BAMO website. Can someone help and explain what is wrong in my thought process.

Thanks
Click to expand...
When they talk about "the sum of the digits of the neighbor(s) of a given circle", they carefully indicate that this applies even when a circle has only one neighbor! (I myself missed that on my first pass through! I only saw that after reading through their explanation a couple times and being baffled by it.)

So in their answer, 1 is the sum of the digits of 10, and 8 is the sum of the digits of 17. In your first one, 3 is not the sum of the digits of 10, and 8 is not the sum of the digits of 15, so it doesn't work. The same is true of the others.

I guess you have to read very, very carefully!
 
I see. Thank you Dr. Peterson. Its problem example 18-23-59-22-46 really make it so confusing =(

thank you again!!!
 
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