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Worksheet generator
Pick what you want, print the page. The answer key comes with it, on its own sheet, and it tells you the mistake behind every wrong choice — not just which letter is right.
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1.All the red boxes are heavy. Box X is not heavy. What must be true?[4]
ABox X is red
BBox X is not red
CBox X is blue
DSome red boxes are light
ENothing can be said about box X
2.A number is doubled, then 6 is added, then the result is halved. The answer is 11. What was the original number?[4]
A4
B8
C11
D16
E22
3.Cards numbered 1 to 10 lie face up. You take any six of them. Must two of your cards add up to 11?[4]
AYes, always
BYes, but only if you take the card numbered 1
CNo, six cards can be chosen that avoid it
DOnly if the six numbers are consecutive
EIt cannot be decided without knowing the cards
4.Seven cups all stand upside down. In one move you must turn over exactly two cups. Can all seven ever stand the right way up?[5]
AYes, in 4 moves
BYes, in 7 moves
CYes, but it takes many moves
DIt depends which two cups you pick
ENo, it is impossible
5.One of nine identical-looking coins is slightly heavier. Using only a balance, what is the smallest number of weighings that is certain to find it?[5]
A1
B2
C3
D4
E8
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 8 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
Answer key — Math Kangaroo practice
Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.
1.B — Box X is not redKA-0099Reading a logical statement precisely
AI read the rule backwards, as if being heavy were what makes a box red.
CI assumed not red must mean one particular other colour, when the rule says nothing about which.
DI contradicted the rule I was given rather than applying it to box X.
EI decided one fact could not settle anything, without testing what would follow if X were red.
2.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.
3.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.
4.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.
5.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.