Who's the Tallest?

10 puzzles in visual logic.

Posted Dec 10, 2019

The term "visual thinking" was coined (as far as I can tell) by the late psychologist and art critic Rudolf Arnheim in his classic 1969 book Visual Thinking. Arnheim’s premise was that: (a) visual thinking is as fundamental to cognition as is verbal thinking, and (b) when we lack the appropriate language to represent some feeling, notion, or intuition, we turn to our capacity to form visual images to help us figure it out.

There is a type of visual thinking that can be called, for lack of a better term, visual logic—not to be confused with this same term as used in computer science. This implies the ability to organize visual concepts or objects in a logical, coherent way. A visual logic puzzle that exemplifies what this entails is sometimes called the “Who’s the Tallest?” puzzle. This requires us to determine the comparative heights of individuals by visualizing them logically. Here is an example:

Meg is taller than Jason, but shorter than Benito. Darlene is shorter than Meg, but taller than Jason. Who’s the tallest of the four?

To visualize the heights in relation to each other, we might want to put the people in a stack—one on top or below the other—according to the stipulations of the puzzle until the order of people in the stack is consistent with the statements. For example, in the stack Meg will be above Jason, since she is taller than he is, but below Benito, since she is shorter. We are told that Darlene is shorter than Meg but taller than Jason. The only place to put her is below Meg and above Jason:

  • BENITO
  • MEG
  • DARLENE
  • JASON

As can now be seen, literally, the tallest of the four is BENITO. The ten puzzles provided here are all solved in this, or a similar, way. They demonstrate what visual logic is and how our diagrams (such as the stack one) are derivatives of this form of reasoning.

Visual languages abound in modern-day society, from graphic design to emoji, indirectly supporting Arnheim’s perspective. There is a saying that I came across recently, of unknown authorship (at least as far as I can tell), that summarizes the importance of visual thinking rather eloquently. It goes somewhat like this: “Only if you can visualize something, can you ever hope to create it.”

Puzzles

For the ten puzzles, you have to determine who is the tallest. They start off easy, becoming increasingly more complex.

1. Sylvia is taller than Samuel, but shorter than Stacy.

2. James is taller than Jasmine, but not Jamila.

3. Amy is shorter than Aaron. Alice is shorter than Amy.

4. Ken is shorter than Krista, but taller than Karen. Krista is shorter than Kyle.

5. Rina is taller than Renata, but shorter than Ron. Rory is also shorter than Ron, but taller than Rina.

6. Vince is shorter than Vera and Vivi, but he is not the shortest. Vasco is shorter than Vivi. But Vivi is not the tallest.

7. Mary is taller than Martha. Mina is taller than Mary. Mack is shorter than Martha.

8. Liam is taller than Lily, who is taller than Leslie, who is taller than Lola. Laura is taller than Liam.

9. Naomi is shorter than Nadia. Ned is taller than Nick and Noah. Ned is not the tallest and Noah is not the shortest.

10. Dina is taller than Darla, but shorter than Dick. Dave is shorter than Darla, but taller than Dana.  Dick is shorter than Dotty.

Answers

1. Stacy

  • STACY
  • SYLVIA
  • SAMUEL

2. Jamila

  • JAMILA
  • JAMES
  • JASMINE

3. Aaron

  • AARON
  • AMY
  • ALICE

4. Kyle

  • KYLE
  • KRISTA
  • KEN
  • KAREN

5. Ron

  • RON
  • RORY
  • RINA
  • RENATA

6. Vera

  • VERA
  • VIVI
  • VINCE
  • VASCO

7. Mina

  • MINA
  • MARY
  • MARTHA
  • MACK

8. Laura

  • LAURA
  • LIAM
  • LILY
  • LESLIE
  • LOLA

9. Nadia

  • NADIA
  • NAOMI
  • NED
  • NOAH
  • NICK

10. Dotty

  • DOTTY
  • DICK
  • DINA
  • DARLA
  • DAVE
  • DANA