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← Punched Cards & a Lights Puzzle

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Lesson 6 of 7

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7 min

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Here is the line to keep from each idea before you answer.

What to keep from a card with holes
IdeaThe line to keep
Numbers on cardsIn binary, each place is worth twice the place on its right. Add the places that have a 1.
Letters on cardsFour holes give 16 patterns. Five holes give 32. So 26 letters need five holes.
Sorting with a needleSort by the 1 hole first and the 16 hole last. Put the open-hole pile behind.
A lights puzzleEach clue keeps only the settings that obey it. When one setting is left, that is the answer.

A five-hole card reads 10100. What number is it?

  • 2, because two holes are open
  • 20, because 16 + 4 = 20
  • 5, because the 1s sit in places 1 and 3

What is the biggest number a five-hole card can show?

  • 32, because five holes make 32 patterns
  • 25, because that is where the places stop
  • 31, because 16 + 8 + 4 + 2 + 1 = 31

Binary places: how does each compare with the one on its right?

  • It is worth twice as much
  • It is worth ten times as much
  • It is worth the same

Which holes do you open to make 21?

  • 16, 4 and 2
  • 16, 8 and 1
  • 16, 4 and 1

Why do 26 letters need five holes?

  • Five holes make exactly 26 different patterns
  • Each letter needs a hole all of its own
  • Four holes give 16 patterns, five give 32

In our code, A is 1. What does the card 11110 show?

  • No letter, because 30 is more than 26
  • The letter D, because four holes are open
  • The letter after Z

A needle goes through one hole of a deck. Which cards fall out?

  • Cards that have that hole shut
  • Cards with the biggest letter
  • Cards that have that hole open

Which hole do you use first to sort five-hole cards?

  • The 1 hole
  • The 16 hole
  • Any hole, because the order does not matter

After a pass, how do you stack the two piles?

  • Open-hole pile in front, shut-hole pile behind
  • Shuffle each pile first
  • Shut-hole pile in front, each pile in order

Five lamps are each ON or OFF. How many settings are there?

  • 32
  • 10
  • 25

The clue "lamp 5 is ON" is X X X X ON. How many of the 32 cards does it keep?

  • 4, because there are four X marks in a row
  • 5, because there are five lamps in the deck
  • 16, because four X marks make 16 patterns

Which clue removes the fewest cards from the deck?

  • Lamp 5 is ON
  • Not all five lamps are ON
  • Lamps 4 and 5 are the same

You can now put a number or letter on a card. You can sort a deck one hole at a time. You can shrink a deck of settings with clues.

Next, Data Visualisation & Analysis turns facts into charts.

Reveal every answer to finish this lesson.