Worksheet generator

1.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.

2.E — No, it is impossibleKA-0028Parity arguments

• AI found a sequence that turned over most of the cups and assumed the last one could be fixed somehow.
• BI matched the number of moves to the number of cups without checking whether the target is reachable at all.
• CI assumed that with enough moves any arrangement can be reached.
• DI thought the choice of which cups to flip could change whether the target is reachable.

3.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.

4.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.

5.D — 12KA-0060Operation puzzles and cryptarithms

• AI added the digits of 132 instead of working out what A and B must be.
• BI found A + B correctly and then halved it, as if the question wanted one digit.
• CI spotted the 11 in the working and gave that instead of the sum it multiplies.
• EI found a pair of digits by trial and misadded them by one.

6.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.

7.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.

8.D — 25KA-0106Inferring a rule from examples

• AI used the rule add 4, which fits the first example but not the others.
• BI found a rule from two examples only and never tested it against the third.
• CI doubled the input and forgot the extra one that every example needs.
• EI used double and add five, which fits none of the examples exactly.

9.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.

10.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.