- Ben’s oldest son was a twin.
- All of Ben’s children were twins except for 41 of them.
- All of Ben’s children were triplets except for 41 of them.
- All of Ben’s 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.
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.
Solution with minimum algebra
