Worksheet generator

1.B — 28KA-0035Handshakes and pairs

• AI doubled the number of people, as if each person made two handshakes in total.
• CI let each person shake hands with all eight people including themselves before halving.
• DI multiplied 8 by 7 and forgot that each handshake was counted from both sides.
• EI multiplied 8 by 8, counting every ordered pair including a person with themselves.

2.C — 4KA-0040The pigeonhole principle

• AI answered with the lucky case, where the first two socks happen to match.
• BI used the number of colours as my answer without adding one for the sock that must repeat.
• DI worked from the number of socks of each colour instead of the number of colours.
• EI took the whole drawer, guaranteeing a pair but far more socks than are needed.

3.C — 48KA-0070Counting with restrictions

• AI treated the twins as one child and forgot they can also swap places with each other.
• BI glued the twins together into a single block but then forgot that the block can be arranged with the others in more ways than I counted.
• DI halved the 120 total, assuming the twins are together in exactly half the arrangements.
• EI counted every arrangement of five children and forgot the twins' condition entirely.

4.A — 12KA-0071Overcount, then correct

• BI divided the 120 arrangements by 6 rather than by the 10 movements that leave a bracelet looking the same.
• CI allowed for turning the bracelet but forgot it can also be flipped over.
• DI halved the 120 for flipping but forgot that turning also gives the same bracelet.
• EI counted every arrangement in a line, as if the bracelet had a fixed first bead.

5.C — 4KA-0140The multiplication principle

• AI counted the codes that do start with A rather than the ones that do not.
• BI counted the letters available for the first position instead of counting whole codes.
• DI counted every arrangement of the three letters and forgot the restriction.
• EI allowed letters to repeat, which the words each exactly once rule out.