Multiple choice

Two dice are rolled one by one. In how many ways is the sum of numbers, occurring on dice, a number of the form u2 + 1 where u is a natural number?

  1. 4

  2. 6

  3. 8

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The possible sums of two dice range from 2 to 12. The numbers of the form u^2 + 1 are 1^2+1=2, 2^2+1=5, and 3^2+1=10. The ways to get 2 are (1,1); to get 5 are (1,4), (2,3), (3,2), (4,1); to get 10 are (4,6), (5,5), (6,4). Counting these gives 1 + 4 + 3 = 8 ways.

AI explanation

When two dice are rolled, the possible sums range from 2 to 12, so we test these sums against the given equation u squared plus 1. The only values from this form that fit the possible sums are 2 (when u is 1), 5 (when u is 2) and 10 (when u is 3). The combinations to roll a sum of 2 are 1, the combinations for a sum of 5 are 4, and the combinations for a sum of 10 are 3. Adding these together gives 1 plus 4 plus 3, resulting in 8 ways.

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