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 — 210KA-0057Clever regrouping (pair to round numbers)

• AI paired the numbers from the outside in but left the 20 out of every pair, so I added only up to 19.
• BI estimated the total as a round number instead of working it out.
• DI used eleven pairs of 20 instead of ten pairs of 21.
• EI multiplied 20 by 21 and forgot that pairing counts every number twice.

3.C — 5KA-0061Operation puzzles and cryptarithms

• AI solved for the triangle and gave that instead of the square.
• BI found the triangle is 4 and gave that number, without going on to the second equation.
• DI halved the 12 instead of dividing it by the three triangles.
• EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.

4.A — 33KA-0171Recursive rules

• BI used the rule 2a(n) - 1 but started the sequence at 1 instead of 2.
• CI doubled six times and ignored the minus one entirely.
• DI stopped at a(5), one term early.
• EI computed 2^6 - 1, applying the minus one only once at the very end.

5.B — 40KA-0080Properties of triangles and quadrilaterals

• AI subtracted 100 from 180 and then divided by four instead of by two.
• CI assumed the two equal angles are always 45 degrees.
• DI gave what is left after taking 100 from 180 without splitting it between the two angles.
• EI made the 100 one of the equal pair, which would already exceed 180 degrees on its own.

6.D — 6KA-0085Line and rotational symmetry

• AI checked only the vertical and horizontal folds and stopped there.
• BI counted the lines through opposite corners and forgot the ones through opposite edges.
• CI assumed a hexagon behaves like a rectangle with a couple of extra folds.
• EI counted each line twice, once from each end.

7.B — 60KA-0093Weighing and balance puzzles

• AI halved the apple's weight, as if one apple balanced two pears.
• CI assumed a pear must weigh the same as an apple because the two sides balance.
• DI multiplied the apple's weight by three halves the wrong way round, making the pear heavier.
• EI gave the total weight of the two apples rather than the weight of one pear.

8.C — 65KA-0103Recursive rules

• AI stopped at the fourth term, counting the starting number as the first step rather than the first term.
• BI generated one term too few, giving the fifth term instead of the sixth.
• DI doubled six times and subtracted 1 only once at the end.
• EI generated one term too many, giving the seventh instead of the sixth.

9.C — 12KA-0105Patterns in tables and grids

• AI stopped at row 3, taking two steps down from the top instead of three.
• BI found where row 4 starts but forgot to move across to the third column.
• DI moved three columns across instead of two, counting columns rather than steps between them.
• EI took four steps of 3 downwards instead of three, counting rows rather than the gaps between them.

10.C — 28KA-0123Eliminate impossible choices by bounding

• AI ruled out the square 6 by 6, forgetting that a square is a rectangle.
• BI did not think to try 4 by 9, so I judged this perimeter impossible.
• DI missed the 3 by 12 rectangle when listing the factor pairs.
• EI stopped listing factor pairs before reaching 2 by 18.

11.C — 8KA-0012Casework

• AI counted each pair of digits once instead of counting both orders, such as 17 and 71.
• BI listed the pairs starting from 1 and 7 and forgot the number 80, where the second digit is zero.
• DI included 08 as a two-digit number, but a two-digit number cannot start with zero.
• EI counted both orders of every pair and then counted the pairs that reverse to themselves twice as well.

12.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.

13.A — 1/10KA-0125Spot the trick vs. decide to grind

• BI cancelled the chain but stopped one factor early, leaving a 9 on the bottom.
• CI worked out the first bracket and assumed the rest made no difference.
• DI gave the last bracket on its own instead of the whole product.
• EI assumed everything cancels completely, leaving nothing behind.

14.C — 25KA-0135Digit-constraint puzzles

• AI counted the odd numbers in one row of ten and treated that as the whole answer.
• BI used four odd digits instead of five, forgetting that 9 is odd.
• DI counted every two-digit number that is itself odd, which only fixes the last digit.
• EI let the first digit be any of ten values rather than only the five odd ones.

15.A — No, because the two removed corners share a colour, so 32 squares of one colour remain and only 30 of the otherKA-0176Coloring arguments

• BI checked that the counts match but a matching count does not make a covering possible.
• CI invented a divisibility condition; dominoes cover two squares, so only divisibility by 2 could matter.
• DI changed the rules rather than testing them; the question says dominoes cover squares sharing an edge.
• EI appealed to the shape, but plenty of non-rectangular regions can be tiled by dominoes.