Worksheet generator

1.D — 75KA-0023The multiplication principle

• AI added the number of options at each step instead of multiplying them.
• BI treated the two digits as one choice of ten rather than two independent choices of five.
• CI assumed the two digits had to be different, so I used 5 times 4 for them.
• EI used 5 choices for the letter position as well, forgetting there are only three letters.

2.D — 24KA-0073Arrangements of a few objects

• AI counted the letters rather than their arrangements.
• BI multiplied 4 by 3 and stopped, forgetting the last two positions.
• CI used 4 choices for every position, as if letters could repeat.
• EI used 4 choices in each of four positions, which allows every letter to repeat.

3.B — 15KA-0074Selections of a few objects

• AI doubled the group size instead of counting pairs.
• CI allowed a student to be paired with themselves, adding six impossible pairs.
• DI counted each pair twice, once in each order, and forgot to halve.
• EI multiplied 6 by 6, counting every ordered pair including a student with themselves.

4.A — 4KA-0154Inclusion–exclusion with two sets

• BI found how many students play at least one of the two and answered with that instead.
• CI added 18 and 15 to get 33, subtracted the 30 in the class, and used the 3 left over.
• DI removed the 7 from both groups and subtracted 11 and 8 from 30, taking the overlap away twice.
• EI answered with the number who play both, which is what the question gave me rather than what it asked for.

5.A — 6KA-0173Counting up to symmetry

• BI counted every colouring of the four edges and forgot that rotations make some of them identical.
• CI divided 16 by 4, but that only works when no painting is left unchanged by a rotation, and some are.
• DI halved 16, treating only the 180 degree turn as a symmetry.
• EI listed by how many edges are black but forgot that two black edges can be adjacent or opposite.

6.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.

7.C — 7KA-0077The pigeonhole principle

• AI answered with the luckiest case, where the first three balls happen to match.
• BI found the worst case of two of each colour and forgot to take one more.
• DI multiplied the three colours by the three balls I need, rather than thinking about the worst case.
• EI worked from the number of balls of each colour rather than from the number of colours.

8.B — 7KA-0157The pigeonhole principle

• AI thought that one more than the number of colours must give three of a kind, which only guarantees a PAIR.
• CI got to two of each colour, then added one more for each colour instead of one more in total.
• DI assumed the worst case meant emptying the largest pile of 12 reds first.
• EI answered with the number of socks I want rather than the number I must take to be sure of them.

9.A — 120KA-0166Counting up to symmetry

• BI counted every arrangement in a row, so each circular seating got counted once for every rotation.
• CI divided 720 by 20 or some other number instead of by the 6 rotations.
• DI divided by 12, treating reflections as identical too, though the question only allows rotations.
• EI fixed two people rather than one, dividing by an extra factor.

10.A — 8KA-0175The pigeonhole principle

• BI used the number of possible remainders without adding one for the pair that must collide.
• CI doubled 7, thinking I needed two full sets of remainders.
• DI doubled 7 and added one, applying the pigeonhole idea to the wrong number of boxes.
• EI guessed from small cases without identifying what the boxes actually are.