Puzzle of the Day: What Does the Night-Sky Equation Equal?

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Shape algebra puzzle on a starry night background. Moon plus moon plus star equals 16. Star plus star plus planet equals 19. Moon plus planet equals 7. Question: star plus moon times planet equals what?
Three night-sky equations and a mystery fourth line to solve
Puzzle image: made for aglena.

A crescent moon, a gold star and a ringed planet each stand for a whole number. Three equations give you everything you need. The fourth line looks easy, but it hides a small trap.

The puzzle

  • Moon + Moon + Star = 16
  • Star + Star + Planet = 19
  • Moon + Planet = 7

What is Star + Moon × Planet?

Show hint

Use the third line to write the planet in terms of the moon, and the first line to write the star in terms of the moon. Then the second line has only one unknown left.

Show answer

Answer: 20.

Answer diagram for the night-sky equations puzzle: moon equals 4, star equals 8, planet equals 3, and the last line, star plus moon times planet, equals 20 because the multiplication comes first: 8 plus 12.
The solved puzzle: multiply first, so the last line is 20
Puzzle image: made for aglena.
  1. From line 3, Planet = 7 − Moon. From line 1, Star = 16 − 2 × Moon.
  2. Put both into line 2: 2 × (16 − 2 × Moon) + (7 − Moon) = 19, so 39 − 5 × Moon = 19 and Moon = 4.
  3. Then Star = 8 and Planet = 3. Check: 4 + 4 + 8 = 16, 8 + 8 + 3 = 19, 4 + 3 = 7.
  4. Multiplication comes before addition, so Star + Moon × Planet = 8 + (4 × 3) = 8 + 12 = 20.

The trap is working left to right: (8 + 4) × 3 gives 36. Without brackets, the multiplication always goes first.

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