Worksheet generator

1.B — 3 centsKA-0010Money and change

• AI found the smallest amount that cannot be made rather than the largest one.
• CI did not notice that 7 is 2 plus 5, so I marked it as impossible without testing it.
• DI only tried using coins of one kind at a time and never mixed the two denominations.
• EI assumed odd amounts are impossible because one of the coins is even.

2.D — ThursdayKA-0021Remainders and modular cycles

• AI found the remainder 2 but counted the two days starting from today rather than starting from tomorrow.
• BI divided 100 by 7 and used the quotient of 14, treating the leftover days as if there were none.
• CI remembered there was a remainder but used a remainder of 1 instead of working it out.
• EI counted 100 divided by 7 as 14 remainder 3 instead of remainder 2.

3.C — 55 degreesKA-0022Angles on lines, in triangles, in polygons

• AI assumed the triangle was isosceles because it had a right angle, so I repeated the 35.
• BI assumed a right-angled triangle always has two 45 degree angles.
• DI subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.
• EI subtracted only the 35 from 180 and forgot to take off the right angle as well.

4.E — 24KA-0038Building and counting with unit cubes

• AI added the three measurements together instead of multiplying them.
• BI counted one layer of 4 by 3 and forgot that the block is two layers tall.
• CI read the block as 3 by 3 by 2 because the drawing hid the far column.
• DI counted only the cubes whose faces I could actually see in the picture.

5.A — 150 degreesKA-0170Angles on lines, in triangles, in polygons

• BI found the exterior angle and answered with that instead of the interior one.
• CI used 360 divided by 12 subtracted from 195, or otherwise slipped a step in the arithmetic.
• DI gave the total of all twelve interior angles rather than one of them.
• EI used a ten-sided polygon by mistake.

6.B — square 3KA-0005Nets and folding, 2D to 3D

• AI picked the square directly next to the shaded one in the net, but neighbours in the net share an edge on the cube.
• CI counted to the far end of the column, assuming the square furthest away in the net is the one opposite.
• DI picked one of the side flaps because it is not touching the shaded square in the drawing.
• EI picked the other side flap for the same reason, without tracking what happens as the net folds.

7.D — 30KA-0007Working backwards

• AI added the 6 and the 9 and stopped, forgetting to undo the halving at the start.
• BI undid the steps in the order they were written instead of reversing the order as well as the operations.
• CI doubled the 9 first and then added the 6, which reverses the steps in the wrong order.
• EI doubled twice because giving half away felt like it should be undone more than once.

8.B — 1KA-0089Building and counting with unit cubes

• AI assumed every small cube touches the outside somewhere.
• CI counted the cubes at the centre of each face, which are painted on one side.
• DI counted the corner cubes, which are the most painted rather than the least.
• EI gave the total number of small cubes instead of the unpainted ones.

9.B — Bo onlyKA-0096Truth-tellers and liars

• AI took Ana's statement at face value without checking whether a truthful person could say it.
• CI decided nobody was lying without testing Ana's statement against that assumption.
• DI believed Ana's statement even after concluding she was a liar, which is what a liar's statement cannot be.
• EI gave up when Ana's statement looked circular, instead of testing one assumption all the way through.

10.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.

11.C — 55KA-0107Growth patterns and figurate numbers

• AI stopped at the eighth triangle, losing count while adding the rows.
• BI gave the ninth triangle instead of the tenth, being one row short.
• DI gave the eleventh triangle, adding one row too many.
• EI squared the position number, which describes square patterns rather than triangular ones.

12.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.

13.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.

14.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.

15.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.