MATHS Riddles

 

Assessment started: undefined.

Item 1

Mr. and Mrs. Heck have five children: four boys and a girl.

They compared their ages among themself and this is what the children said:

• Adrian: "I am the second, counting either from the oldest or the youngest."
   
• Bernadette: "I have at least one younger brother."
   
• Jake: "I am two places older than my sister, Bernadette."
  (i.e., there is one sibling older than Bernadette but younger than Jake)
   
• Doug: "Bernadette is my younger sister."
   
• Enrique: "I am the...."

Unfortunately, Enrique was interrupted. Can you complete his sentence?

• Youngest
• 4th${\mathbf{4}}^{\mathbf{\text{th}}}$ inline
• Oldest
• Only elder brother of BernadettaSolution

  There are three possibilities for the positions (in order of birth) of Jake and Bernadette:
  1st$1^{\text{st}}$ and 3rd$3^{\text{rd}}$
  2nd$2^{\text{nd}}$ and 4th$4^{\text{th}}$
  3rd$3^{\text{rd}}$ and 5th$5^{\text{th}}$
  The second possibility is out as we see that Adrian is either 2nd$2^{\text{nd}}$ or 4th$4^{\text{th}}$ so if the second possibility is the case, then there is no possible position for Adrian. The third possibility is also out as Bernadette has at least one younger brother so she cannot be the youngest. This leaves us with the first possibility where Jake is the oldest and Bernadette is the middle child.

  We also see that Doug is older than Bernadette, the 3rd$3^{\text{rd}}$ child. The first place has already been taken by Jake so Doug must be the second oldest. Adrian is either 2nd$2^{\text{nd}}$ or 4th$4^{\text{th}}$ but 2nd$2^{\text{nd}}$ has been taken by Doug so Adrian is the second youngest. The only vacancy left for Enrique is the 5th$5^{\text{th}}$ child. In other words, Enrique is the youngest.