Question

The yellow squares in the grid contains numbers from 1-10 each number used only once

The green squares contain products of the number in their adjacent yellow squares​

Answer 1

Given : The yellow squares in the grid contains numbers from 1-10 each number used only once . The green squares contain products of the number in their adjacent yellow squares​

To find :  Fill Yellow Square

Solution:

Yellow Square between 378 , 144 , 90 & 40 should be HCF of all these or factor of HCF

HCF  of 378 , 144 , 90 & 40 is 2

Hence yellow  Square between 378 , 144 , 90 & 40

would be 2 or 1

Case 1 : Lets assume its 2

Then two remaining  adjacent yellow Sqaure of 40 should have multiplication

40/2 = 20

20 = 4 * 5    only possibilty    as 2 * 10  ( 2 is already used)

5 is not  a factor 144

hence 4  will be below 144  &  5 will be below 90

in 60 remaining possible factor  

2 * 6   , 3 * 4  ( but 2 & 4 already used)

Hence this solution is not possible

Case 2 :  Lets assume its 1

40 can be  8 * 5  only

8 will be below  144   ( as 5 is not factor of 144)

5 will be below   90

160  can  have now  2* 10     ( 4 * 5 not possible as 5 already used )

10 is not factor of 144

hence 10 will adjacent to 60

& 2 will be adjacent to 144

remaining adjacent to 144 = (144/ (2 *  8 * 1)  = 9

7 is  only factor in 378  hence 7 will be at top

remaining factor of 378 = 378 / (9 * 7 * 1)  = 6

Adjacent to 90 = 90/(6 * 1 * 5)  = 3

Adjacent to 60  =  60/(3 * 5)  = 4

                        7

                9      378     6

       2     144     1         90     3

10   160     8      40      5      60    4

378 = 9 * 7 * 6  * 1

144 = 9 * 8 * 2 * 1

90  = 6 * 5 * 3 * 1

160 = 10 * 8 * 2

40  = 8 * 5 * 1

60  = 5 * 4 * 4

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