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How many children? (Posted on 2013-09-02) Difficulty: 2 of 5
  1. Benís oldest son was a twin.
  2. All of Benís children were twins except for 41 of them.
  3. All of Benís children were triplets except for 41 of them.
  4. All of Benís children were quadruplets except for 41 of them.
How many children did Ben have?

*** Counting triplets as twins or, quadruplets as triplets is not permissible.

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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Solution Solution with minimum algebra Comment 6 of 6 |
From statements 2, 3, and 4 the number of twins equals the number of triplets equals number of quadruplets.

Since we have an equal number of twins, triplets and quadruplets the number of each is a multiple of the least common multiple of 2, 3, and 4: 12.

Let 12x be the number of twins/triplets/quadruplets.  Then 41 = singles + 12x + 12x and the total number of children equals 41 + 12x.

From statement 1 x must be at least 1, but x cannot be higher than 1 otherwise there would be a negative number of single children.

Therefore x=1, which makes the total number of children 41 + 12*1 = 53.

  Posted by Brian Smith on 2018-12-17 13:03:01
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