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The faces of a standard die are numbered 1, 2, 3, 4, 5, and 6 such that the sum of the numbers on any two opposite faces is 7. Tia writes one number on each vertex of the die such that the number on each face of the die is the greatest common divisor of the numbers at the four vertices of that face. What is the smallest possible sum of the eight numbers Tia writes?

 

I believe the answer is 6 (GCD(3,2,1) + 12 (GCD(6,4,2) + 60 (GCD(6,5,4) + 6(GCD(6,3,2) + 30 (GCD(3,5,6) + 15(GCD(5,3,1) + 20(GCD(1,4,5) + 4(GCD(1,2,4)

 

SO the answer is 153, but can someone check this for me? (PLEASE)

 Sep 6, 2022
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PLEASE NOTE: I accidentally wrote GCD over their when I meant LCM

 

BTW:

60,12,6,30 GCD = 6

30,15,20,60 GCD = 5

60,12,4,20 GCD = 4

6,30,15,6 GCD = 3

6,12,4,6 GCD = 2

4,6,15,20 GCD = 1

 

so 60+30+20+15+12+6+6+4=153

 Sep 6, 2022

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