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Mathematical Logic

Find the Order


Three racing snails named Molly, Nick and Orlando have a fierce competition in the 10 centimeter run.

Nick and Molly did not place next to each other. Who came in \( 2^\text{nd} \) place?

How many ways are there to arrange the three cards above in a row so the 7 is to the left of the 8? (The 7 may be one or two cards away from the 8.)

Azizi, Blanche, Clio, and Daaiyah had a hot-air balloon race. Based on the clues below, who placed \( 1^\text{st} ?\)

  1. Azizi beat at least one of the competitors.

  2. Both Blanche and Clio each beat at least two of the competitors.

  3. Azizi and Clio did not finish next to each other.

Azizi, Blanche, Clio, and Daaiyah had another race, this time in Formula One cars. Based on the clues below, who placed \( 1^\text{st} ?\)

  1. None of the racers finished in the same place as their names when listed using alphabetical order; that is, Azizi didn't finish \( 1^\text{st} ,\) Blanche didn't finish \( 2^\text{nd} ,\) Clio didn't finish \( 3^\text{rd} ,\) and Daaiyah didn't finish \( 4^\text{th} .\)

  2. Blanche didn't finish two places apart from Daaiyah.

  3. Azizi finished ahead of Daaiyah.

The ace of diamonds, king of hearts, queen of clubs and joker from a deck of cards are placed face down in a 2 by 2 square as shown.

Based on the clues, where is the queen?

  1. The ace is not in the lower right corner.

  2. The king is further to the left than joker (and may or may not be on the same row).

  3. The queen is higher up than the ace (and may or may not be on the same column).

Xandra, Yu, and Zhao are the only participants in a cake-baking competition which is scored in two separate categories: Design and Taste.

Based on the clues below, where did Yu place in Design and Taste?

  1. None of the participants placed the same in both categories.

  2. Xandra beat Zhao in both categories.

  3. Yu didn't lose in the Taste category.


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