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The Height That Did Not Match the Photo (illustration)
FILE No.29Unsolved

The Height That Did Not Match the Photo

Difficulty ★★☆about 4 minFloor Plans & LayoutsFinding the premiseSame object, different view
A photo shows eight floors; a survey says ten to eleven floors high. Neither is wrong. Why?

Case Record

In a survey of a building, two documents were collected.

Photo taken by Aoki: It shows the building from its foot to the roof, and counting gives what looks like an 8-story building.

Sakata’s survey report: "I measured the height from the foot of the building to the roof. It corresponds to 10 to 11 floors of an ordinary building."

The two examined the same building. The photo is unedited and the measurement has no error. Each floor is the same height as in an ordinary building.

Your question

Why do the photo and the report seem to disagree?

Case Files

The photo Aoki took

The photo Aoki took

Timeline

  1. Aoki photographs the building.
  2. Sakata measures the building and reports.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

Where on the same building did each person look or measure?

Open hint 2

Can the “foot” of a building be at different heights depending on the place?

Open hint 3

Was the ground each stood on at the same height?

Solve It

Your question

Why do the photo and the report seem to disagree?

Choose the answer closest to the truth.

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The Truth

The building stands on a mountain slope

The answer is “the building stands on a mountain slope.”

Aoki shot from the higher ground on the hill side, and Sakata measured from the lower ground on the opposite side. On the hill side the lower floors are hidden by the ground, so only eight floors show. On the low side, more floors continue below. An atrium does not change the number of floors, and shooting from afar does not change it either. Skipped floor numbers cannot explain the gap if each floor is the same height.

Why the numbers differBoth documents are accurateThe building stands on a slopeThe hill side hides the lower floorsAnswer: a mountain slope
Diagram of the solution

Key Points

  • Separate the range seen in the photo from the range measured
  • Even for one building, the “foot” differs by viewpoint
  • When unedited, error-free documents disagree, look for a difference in premise

Why people get fooled

You assume the “foot of the building” is one place and do not consider that ground height can differ.

Similar tricks

  • Finding the premise behind conflicting documents
  • Thinking of what a photo does not show

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