MO Z6-6-1

Write integers greater than 1 to the blanks in the following figure, so that each darker box was product of the numbers in the neighboring lighter boxes. What number is in the middle box?

Result

x =  245025

Solution:

55=5⋅ 11 99=9⋅ 11 45=5⋅ 9 x=45⋅ 99⋅ 55=24502555=5 \cdot \ 11 \ \\ 99=9 \cdot \ 11 \ \\ 45=5 \cdot \ 9 \ \\ x=45 \cdot \ 99 \cdot \ 55=245025

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