Brilliant Aarti

Logic Level 2

My daughter Aarti, aged 4, was seeing 6-sided dice for the first time. I rolled 2 dice and asked her to count the visible dots. To my utter surprise she replied, "36". I was sure that she did not know multiplication yet. On closer examination, it dawned on me that she had actually added all the visible dots, even the ones on the vertical sides of the dice. Knowing that the dots on the opposite faces of a dice add-up to 7, what was the sum of numbers on the top face of the 2 dice rolled?

7 8 9 6 12 5

Rajen Kapur by Rajen Kapur , 72, India

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3 solutions

The sum of the numbers on one die is 21 (6+5+4+3+2+1). The sum of all numbers on two dice is 42. Since Aarti counted only 36, a sum of 6 was not visible (bottom of the dice). A number added to the number on the opposite side of a die is 7. 6 =2*7 - (the sum on the top of the dice). The answer must be 14-6=8.

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Total number of dots on one die = 6 + 5 + 4 + 3 + 2 + 1 = 21 21

So total on both dice = 21 x 2 = 42 42

Since Aarti counted 36 visible dots, the total number of dots at the bottom is 42 - 36 = 6 6

The sum of the total number of dots on the bottom and on the top should be 2 x 7 (for two dice) = 14 14

Since the sum at the bottom is 6 6 , the sum at the top is 14 − 6 = 8 14 - 6 = \boxed{8}

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Raj Magesh
Jul 2, 2015

There are four pairs of vertical sides for the two dice, with a total of 4 × 7 = 28 4 \times 7 = 28 dots. So the number of dots above should be 36 − 28 = 8 36-28=\boxed{8} .

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