Problem 563

[PhilLeTaxi]

It is stated that "The target area of 889200 is the smallest area which can be manufactured in three different variants".

This number seems to be compliant with the problem requirements for M(3) and smaller than 889200 :
865800 = 888 x 975 = 900 x 962 = 925 x 936

Could someone explain why it is not correct ?

[mdean]

It is stated that "The target area of 889200 is the smallest area which can be manufactured in three different variants".

This number seems to be compliant with the problem requirements for M(3) and smaller than 889200 :
865800 = 888 x 975 = 900 x 962 = 925 x 936

Could someone explain why it is not correct ?

Without really delving into the problem, my guess would be the dimension of 962 would be an issue.

[mpiotte]

It is stated that "The target area of 889200 is the smallest area which can be manufactured in three different variants".

This number seems to be compliant with the problem requirements for M(3) and smaller than 889200 :
865800 = 888 x 975 = 900 x 962 = 925 x 936

Could someone explain why it is not correct ?

These dimensions cannot be assembled by the robots starting from unit squares and assembling rectangles made up of 25 or less smaller rectangles.

[PhilLeTaxi]

I don't see why there is an issue with 962.

888 x 1.1 = 976.8 Then 975 is compliant.
900 x 1.1 = 990 Then 962 is compliant.
925 x 1.1 = 1017.5 then 936 is compliant.

888 x 975 = 900 x 962 = 925 x 936 = 865800

The divisor of 865800 lower than 888 is 780 which is not compliant as 780 x 1110 = 865800
Then is leaves the 3 possibilities listed above.

[PhilLeTaxi]

@ mpiotte:

OK thanks for your response.

[apovalyaev]

I don't see why there is an issue with 962.

888 x 1.1 = 976.8 Then 975 is compliant.
900 x 1.1 = 990 Then 962 is compliant.
925 x 1.1 = 1017.5 then 936 is compliant.

888 x 975 = 900 x 962 = 925 x 936 = 865800

The divisor of 865800 lower than 888 is 780 which is not compliant as 780 x 1110 = 865800
Then is leaves the 3 possibilities listed above.

Following the same logic 889200 doesn't suit also, because it can be constructed as 7410x120

[sjhillier]

Following the same logic 889200 doesn't suit also, because it can be constructed as 7410x120

Sorry, it's unclear to me if this is a question or an answer. The original question was answered, the answer being that the length 962 is impossible to manufacture under the stated production constraints. If you are still unsure as to the meaning, please ask again.

[apovalyaev]

Following the same logic 889200 doesn't suit also, because it can be constructed as 7410x120

Sorry, it's unclear to me if this is a question or an answer. The original question was answered, the answer being that the length 962 is impossible to manufacture under the stated production constraints. If you are still unsure as to the meaning, please ask again.

(1) It's a kind of note. Because during the previous post, the following statement "... The divisor of 865800 lower than 888 is 780 which is not compliant as 780 x 1110 = 865800 ..." was used as an argument. And from this statement, it looks like we somehow consider dividers which are outside of "1/1.1" bounds. And if this is the case, I've just note that, for example, for 889200 has much more "1/1.1" divider pairs then three.

(2) And from my side, this is a separate question to confirm. Can each of 2..25 numbers only once participate (can be only part of one dividers)? In other word, can we use such deviders like (23x23x...)x(17x17x...)?

[sjhillier]

(2) And from my side, this is a separate question to confirm. Can each of 2..25 numbers only once participate (can be only part of one dividers)? In other word, can we use such deviders like (23x23x...)x(17x17x...)?

Thanks for the note. On your second question, yes these are allowed.