Error Detection (Parity Magic Trick) — Quiz

Multiple Choice Questions

1. What size grid do the children first lay out their cards in before adding extra parity cards?
A) 4 × 4
B) 5 × 5
C) 6 × 6
D) 10 × 10

2. In the card trick, what is the special extra card added to each row and column called?
A) A magic card
B) A checksum card
C) A parity card
D) A binary card

3. In this activity, what rule must be true about the number of coloured cards in every row and column?
A) It must be an odd number
B) It must be an even number
C) It must equal exactly 5
D) It doesn't matter

4. When one card is flipped, what happens to its row and column?
A) They stay even
B) They become odd in number of coloured cards
C) They disappear
D) They become the same colour

5. According to the resource, which of these is NOT one of the "two states" objects suggested for extension activities?
A) Playing cards
B) Coins (heads or tails)
C) Cards with 0 or 1 printed on them
D) Dice with six sides

6. What real-life number system uses a check digit similar to the parity idea in this activity?
A) Postal codes
B) ISBN (book codes)
C) Phone numbers
D) Credit card PINs

7. In the ISBN checksum method, what is the first digit multiplied by?
A) 2
B) 5
C) 9
D) 10

8. What happens if TWO cards are flipped instead of one?
A) It is always impossible to tell anything went wrong
B) You can always know exactly which two cards changed
C) You can usually narrow it down to one of two pairs, but not always identify the exact cards
D) The parity cards fix themselves automatically

Short Answer Questions

9. Explain why banks and computers need a way to detect errors when data is transmitted. Use the example from the resource about depositing cash.

10. What special character is used in an ISBN when the checksum works out to be a value of 10? Why is this needed?

11. Describe what kind of digit-change error in an ISBN checksum might NOT be detected. (Hint: think about what happens to the sum when one digit goes up and another goes down.)

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Answer Key

1. B) 5 × 5
2. C) A parity card
3. B) It must be an even number
4. B) They become odd in number of coloured cards
5. D) Dice with six sides
6. B) ISBN (book codes)
7. D) 10
8. C) You can usually narrow it down to one of two pairs, but not always identify the exact cards

1. Sample answer: When data such as a bank deposit amount is sent electronically, interference on the line could accidentally change the number (e.g., $10 becoming $1,000). Errors must be detected because they could cause serious mistakes, and computers can't always simply ask for the data to be resent (e.g., signals from deep space probes take too long to retransmit).

1. The letter X is used when the checksum calculation results in the value 10, since a single digit cannot represent "10."

1. If one digit in the ISBN increases while another digit decreases by a matching amount, the total sum used to calculate the checksum might stay the same, so the error would go undetected.