Worksheet generator

1.B — 1KA-0017Truth-tellers and liars

• AI assumed everyone could be lying at once without checking that Cal's statement would then be true.
• CI found one consistent truth-teller and added another without testing whether both could hold together.
• DI assumed everyone was telling the truth without noticing that Ana's statement then contradicts Bo's.
• EI gave up after one assumption led to a contradiction, instead of trying the other assumption.

2.D — 19KA-0018Complementary counting

• AI counted the codes that avoid 3 entirely and gave that as my answer without subtracting.
• BI counted the codes with a 3 in the first position only and forgot the other two positions.
• CI counted the codes with exactly one 3 and forgot the ones with two or three of them.
• EI counted every possible code and forgot to remove the ones with no 3 at all.

3.C — 6KA-0025Counting up to symmetry

• AI also treated bracelets that are mirror images as the same, but only rotations were allowed.
• BI divided the number of beads by itself rather than dividing the number of arrangements by the number of rotations.
• DI divided the 24 arrangements by 2 instead of by the 4 rotations of a circle of four beads.
• EI counted every arrangement in a line and forgot that rotating a bracelet gives the same bracelet.

4.E — 9KA-0037Last-digit behavior of products and powers

• AI assumed a number this large has no reachable last digit and gave up on the cycle.
• BI found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.
• CI found the cycle but counted its positions starting at zero, shifting my answer along by one.
• DI assumed the units digit of any power of 7 is always 7.

5.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.

6.B — 6KA-0045Back-solve from the answer choices

• AI tested the smallest choice first and stopped at the first one that felt about right.
• CI read a third of itself as three times itself and solved the wrong equation.
• DI reversed the comparison, finding a number whose third is 4 less than itself in the wrong direction.
• EI picked the largest choice because dividing by three made me expect a big starting number.

7.D — 30KA-0047Counting by position (sliding window)

• AI counted only the sixteen smallest squares and stopped there.
• BI counted the small squares and the single big one, and forgot every size in between.
• CI counted the 2 by 2 squares as four rather than nine, splitting the board into blocks.
• EI used 4 by 4 positions for every size instead of shrinking the range as the square grows.

8.A — Yes, and many orders workKA-0049Parity of numbers (odd/even behavior)

• BI found one arrangement that works and assumed a problem this fiddly could only have one answer.
• CI saw five odd numbers against four even ones and called that a mismatch, when a row of nine needs exactly five of one and four of the other.
• DI blamed the length of the row rather than checking how many odd and even numbers it has to hold.
• EI decided the first number settles it without checking that starting even would need five even numbers, and only four exist.

9.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.

10.B — 252KA-0075Complementary counting

• AI counted the numbers made entirely of digits other than 7 in every position, including a leading zero.
• CI counted the numbers with a 7 in each position separately and forgot that some were counted twice.
• DI added three lots of 90 and one extra hundred, double counting the 700s.
• EI counted the numbers with no 7 at all and gave that instead of subtracting it.

11.C — 12KA-0090Counting cubes in a stack, including hidden ones

• AI counted the middle cube of each face, which has exactly one painted face rather than two.
• BI counted the corner cubes, which have three painted faces.
• DI counted every cube that is painted at all except the corners, without separating one face from two.
• EI gave the total number of small cubes rather than the ones with exactly two painted faces.

12.B — 2KA-0094Weighing and balance puzzles

• AI assumed one weighing could separate nine possibilities, but it has only three outcomes.
• CI split the coins into halves each time, which wastes the balance's third outcome.
• DI weighed the coins one against another in pairs rather than in groups.
• EI compared each coin with a known good one in turn, which always works but is nowhere near the fewest.

13.B — 9KA-0095The extremal principle

• AI divided 100 by 12 and rounded down instead of up.
• CI rounded the division to a convenient number without checking that a packing with a smaller maximum exists.
• DI gave the number of boxes as the answer rather than a number of apples.
• EI described the case where one box holds everything, which is possible but not guaranteed.

14.D — No, because the number of moves is oddKA-0097Parity arguments

• AI assumed enough moves can undo anything, without asking what each move preserves.
• BI tried a few sequences that nearly worked and assumed a better choice would finish the job.
• CI reached for the number of items rather than for what a single swap actually changes.
• EI thought the choice of swaps could change the outcome, when every swap has the same effect.

15.C — No, the last number is always evenKA-0098Invariants and monovariants

• AI found sequences ending in small numbers and assumed 1 was among the reachable ones.
• BI assumed a hard-looking question must have exactly one answer.
• DI found one sequence ending in 0 and assumed every sequence must end there.
• EI thought the order could change the outcome, when the quantity that decides it never changes.

16.B — 11KA-0112Mixtures and weighted averages

• AI averaged the two averages, ignoring that the classes are different sizes.
• CI weighted the averages but used the wrong class size against each one.
• DI leaned towards the larger class's average without computing the totals.
• EI added the two averages together instead of combining them.

17.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.

18.B — Answer it with your best guess, mark it, and move onKA-0126Time triage: now, later, or guess

• AI let the time already spent decide, but that time is gone whatever I do next.
• CI moved on but left a blank, which scores nothing if I never get back to it.
• DI spent time re-reading work I had no reason to doubt, while 21 unseen questions waited.
• EI assumed the hardest questions are the best use of time, when the unseen easy ones are worth the same each.

19.D — 8KA-0134Paper folding and hole punching

• AI forgot that the punch goes through every layer, not just the top one.
• BI undid only one of the two folds before counting.
• CI doubled twice for the folds but added the second hole instead of doubling for it too.
• EI counted three folds instead of two, doubling one time too many.

20.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.

21.D — DeeKA-0136Ordering and ranking from clues

• AI ignored the very first clue, which rules Ana out of the front directly.
• BI put Bo at the front, but Bo must have Ana immediately in front of him.
• CI forgot that Cal is fixed at the back of the line.
• EI stopped once two arrangements seemed possible, without testing whether the second one actually fits every clue.

22.C — 750KA-0137Multi-step arithmetic word problems

• AI poured out half instead of a third and then forgot to add the 150 ml back.
• BI poured out the third correctly but never added the 150 ml.
• DI assumed the 150 ml added back was the same as the amount poured out, so nothing changed.
• EI added the 150 ml to the full jug without pouring anything out first.

23.D — 49KA-0138Growth patterns and figurate numbers

• AI continued the pattern to the fifth square instead of the seventh.
• BI stopped one square short, giving the sixth instead of the seventh.
• CI added 6 to the sixth square's 36, treating the differences as constant.
• EI continued one square too far and gave the eighth.

24.C — 14KA-0139Dice and cube face relationships

• AI subtracted only the top face from 21, forgetting the hidden bottom face as well.
• BI guessed four middling numbers and added them without using the total of all six faces.
• DI subtracted only the bottom face of 4 from the total of 21.
• EI added the four largest numbers on the die rather than the four that are actually at the sides.

25.B — 9KA-0158Last-digit behavior of products and powers

• AI used the first entry of the cycle because 2026 is even, without working out where in the cycle it lands.
• CI counted the cycle starting from zero, so a remainder of 2 put me one place too far along.
• DI assumed a power that large must end in 1.
• EI multiplied 3 by 2 and used the last digit of that.

26.A — 2 hours 24 minutesKA-0159Combined work rates

• BI averaged the two times, but two taps together must be faster than either one alone.
• CI added the two times, which would be right for filling two tanks one after the other.
• DI halved the smaller of the two times, guessing that two taps must simply be twice as fast as one.
• EI found 2 hours 24 minutes correctly and then halved it a second time.

27.A — It is always oddKA-0167Parity arguments

• BI checked the parity of the count of numbers rather than of their sum.
• CI tried two examples, got different answers, and concluded nothing is forced.
• DI assumed differences must shrink all the way to nothing.
• EI found one sequence of moves ending at 1 and assumed every sequence must.

28.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.

29.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.

30.A — 54KA-0177Overcount, then correct

• BI counted every line joining two vertices and forgot to remove the 12 sides.
• CI counted each diagonal from both of its endpoints and forgot to halve.
• DI used 12 x 10 without halving, double counting every diagonal.
• EI subtracted 24 rather than 12, removing each side twice.