Worksheet generator

1.C — 16KA-0050Working backwards

• AI added the 4 and the 6 and stopped, forgetting to undo the halving.
• BI doubled the 6 first and then added the 4, reversing the steps in the wrong order.
• DI doubled the total at the end rather than doubling only the amount left after the first spend.
• EI doubled twice because spending half felt like it needed undoing more than once.

2.C — CalKA-0091Elimination grids

• AI used Bo's clue and forgot the very first clue, which rules Ana out directly.
• BI read Bo's clue as telling me what Bo has rather than what Bo does not have.
• DI stopped after using each clue once, without going back to see what the ticks had ruled out.
• EI applied Bo's clue but never came back to Ana's, so I left two people in the running.

3.B — BoKA-0092Ordering and ranking from clues

• AI gave the child who is first rather than the one who is second.
• CI placed Cal directly after Ana, reading ahead of Dee as meaning immediately ahead.
• DI built the order backwards from the last position instead of forwards from the first.
• EI assumed the clues left several orders open without checking that they chain into a single one.

4.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.

5.B — 8KA-0100Working backwards

• AI undid the operations in the order they were written instead of in reverse order.
• CI gave the final answer back, assuming the three steps cancelled each other out.
• DI doubled the 11 and subtracted the 6 but forgot the final halving that undoes the doubling.
• EI undid only the halving and stopped there without touching the other two steps.

6.A — Yes, alwaysKA-0102Informal proof by contradiction

• BI found one pair that works and assumed the argument depended on that particular card.
• CI tried a couple of selections, did not find a pair, and stopped looking.
• DI looked for a pattern in the numbers rather than at how many pairs there are to avoid.
• EI thought the answer depended on which six were taken, when the counting settles it for every choice.

7.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.

8.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.

9.D — No, because the two colours cannot balanceKA-0101Coloring arguments

• AI checked that 100 divides by 4 and treated that as proof that a covering exists.
• BI assumed a covering must exist somewhere and that I simply had not found it yet.
• CI gave a reason that is not even true, since 100 really is a multiple of 4.
• EI thought orientation could rescue it, but every turn of a T covers the same mixture of colours.

10.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.