Question

Six dice are stacked on the floor as shown in the figure. On each dice the sum of numbers on opposite face is 7 i.e if one is written on one face then 6 is written on the opposite face and so on.
What is the maximum possible sum of numbers on the 21 visible faces. ​

Answer 1

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

❏ Question:-

@ Six dice are stacked on the floor as shown in the figure. On each dice the sum of numbers on opposite face is 7 i.e if one is written on one face then 6 is written on the opposite face and so on.What is the maximum possible sum of numbers on the 21 visible faces.

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

❏ Solution:-

✏ Given:-

• six dice are stacked on the floor,
• On each dice the sum of numbers on opposite face is 7

( i.e if one is written on one face then 6 is written on the opposite face )

✏ To Find:-

• maximum possible sum of numbers on the 21 visible faces.

✏ Explanation :-

Now,

• Sum of numbers on top dice

✏ 6 + 2×(sum of opposite faces)

✏ 6 + 2×(7)

✏ 6 + 14

✏ 20

• Sum of numbers on left side dice in the middle position

✏ 6 + 1× (sum of opposite faces)

✏ 6 + 1×7

✏ 6+7

✏ 13

• Sum of numbers on right side dice in the middle position

✏ 6 + 1×( sum of opposite sides)

✏ 6 + 1×7

✏ 6 + 7

✏ 13

• Sum of numbers on right side dice in the bottom position

✏ 6 + 5 + sum of opposite faces

✏ 11 + 7

✏ 18

• Sum of numbers of middle dice in the bottom position

✏ sum of opposite faces

✏ 7

• Sum of numbers on left side dice in the bottom position

✏ 6 + 5 + sum of opposite faces

✏ 11 + 7

✏ 18

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

∴ Total sum

= 20 + 13 + 13 + 18 + 7 + 18

= 89

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

Answer 2

$\huge\mathbb{SOLUTION:-}$

$:\mathtt\blue{Sum \: of \: numbers \: on \: top \: dice = 20}$

$:\mathtt\blue{Sum \: of \: numbers \: on \: left \: side \: dice \: in \: middle \: row = 13}$

$:\mathtt\blue{Sum \: of \: numbers \: on \: right \: side \: dice \: in \: middle \: row = 13}$

$:\mathtt\blue{Sum \: of \: numbers \: on \: left \: side \: dice \: in \: last \: row = 18}$

$:\mathtt\blue{Sum \: of \: numbers \: on \: middle \: dice \: in \: last \: row = 7}$

$:\mathtt\blue{Sum \: of \: numbers \: on \: right \: side \: dice \: in \: last \: row = 18}$

$:\mathtt\red{Total \: sum = 20 + 13 + 13 + 18 + 7 + 18 = 89}$