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.E — 60KA-0026Percentages and simple discounts

• AI worked out the size of the discount and gave that as the new price instead of subtracting it.
• BI treated a quarter off as half off and took the price down to 40.
• CI applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.
• DI subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.

4.C — 90 degreesKA-0032Clock geometry: hands, angles, times

• AI gave the angle for one hour mark instead of the three hour marks between the hands.
• BI divided the right angle in half, as if a quarter of the clock were 45 degrees.
• DI used a third of the clock face rather than a quarter of it.
• EI read 3 o'clock as the hands pointing in opposite directions.

5.B — 28KA-0035Handshakes and pairs

• AI doubled the number of people, as if each person made two handshakes in total.
• CI let each person shake hands with all eight people including themselves before halving.
• DI multiplied 8 by 7 and forgot that each handshake was counted from both sides.
• EI multiplied 8 by 8, counting every ordered pair including a person with themselves.

6.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing

• AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
• BI added the two intervals together rather than looking for a time that is a multiple of both.
• DI found a common multiple but not the least one, landing on a later coincidence.
• EI multiplied the two intervals together instead of finding their least common multiple.

7.C — 14KA-0051Complementary counting

• AI counted the multiples of 3 and gave that instead of the numbers that are not multiples.
• BI counted 21 as a multiple of 3 inside the range, so I removed one too many.
• DI removed only the multiples of 3 that are also even, so I subtracted three instead of six.
• EI gave the size of the whole range and forgot to remove anything at all.

8.B — 24KA-0083Perimeter and area of rectilinear shapes

• AI subtracted 6 from 20 and gave that, which is neither a side nor an area.
• CI took the other side to be 20 minus 6 divided by 2, forgetting there are two sides of each length.
• DI multiplied the perimeter by half the known side instead of finding the missing side first.
• EI used 16 as the other side, taking 20 minus 6 plus 2 rather than working from the perimeter properly.

9.E — 8KA-0143Systematic listing

• AI counted the two available digits rather than the numbers they can build.
• BI counted the three positions instead of the numbers.
• CI used only two of the three positions when multiplying.
• DI multiplied 2 by 3, mixing the number of digits with the number of positions.

10.E — Not all birds can flyKA-0146Reading a logical statement precisely

• AI read some cannot as meaning none can, which is a far stronger claim.
• BI chose a statement that directly contradicts the one I was given.
• CI read some as meaning a majority, when it only guarantees at least one.
• DI read some as meaning exactly one, when it means at least one.

11.C — 4KA-0161Remainders and modular cycles

• AI assumed the cycle ends on 1 at every exponent that is a multiple of 2.
• BI used a remainder of 1 rather than 2 when dividing 50 by 3.
• DI doubled my way to 2 cubed = 8 and used 8 minus 2.
• EI assumed a large power of 2 must eventually be divisible by 7.

12.A — 2 hoursKA-0162Rate, time, distance

• BI used only the slower car's speed and divided 300 by 90 the wrong way round.
• CI averaged the two speeds to 75 km/h and divided 300 by it, which ignores that both cars move at once.
• DI divided 300 by 60, using only the slower car.
• EI halved the distance to 150 and then divided by 150, applying the closing speed twice.

13.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.

14.B — 2KA-0016Dice and cube face relationships

• AI used the upper die's touching face instead of the lower one, so I worked from 3 rather than 5.
• CI gave the number on a touching face itself rather than the number opposite it.
• DI subtracted 3 from 7 because I confused which die was sitting on which.
• EI gave the lower die's upward face, which is the number I was told, not the hidden one underneath.

15.B — 4% lowerKA-0065Percentages and simple discounts

• AI applied only the decrease and forgot that the price had already risen.
• CI assumed a rise and a fall of the same percentage cancel each other out exactly.
• DI got the size of the change right but the direction wrong.
• EI added the two percentages together instead of applying them one after the other.

16.C — 11KA-0066Means, and working backwards from a mean

• AI assumed the missing number must be the mean itself.
• BI averaged the three known numbers instead of working from the total.
• DI repeated one of the numbers already given rather than computing the missing one.
• EI used a total of 37 instead of 36, adding the mean in once too often.

17.B — 15KA-0074Selections of a few objects

• AI doubled the group size instead of counting pairs.
• CI allowed a student to be paired with themselves, adding six impossible pairs.
• DI counted each pair twice, once in each order, and forgot to halve.
• EI multiplied 6 by 6, counting every ordered pair including a student with themselves.

18.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.

19.C — 150KA-0117Rate, time, distance

• AI divided 150 by 60 and read the answer as minutes rather than hours.
• BI used 1.5 hours instead of 2.5, dividing 90 by 60 rather than 150.
• DI converted 2.5 hours as two hours and fifty minutes.
• EI multiplied the distance by 60 instead of dividing, then converted.

20.C — 8KA-0147Circles: radius, diameter, and touching circles

• AI subtracted the radii, which is the answer when one circle sits inside the other.
• BI averaged the two radii instead of adding them.
• DI multiplied the radii together rather than adding them.
• EI added the two diameters instead of the two radii.

21.D — 120KA-0148Clock geometry: hands, angles, times

• AI gave the angle for a single hour mark rather than the four marks between the hands.
• BI counted two hour marks instead of four.
• CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
• EI measured the angle the long way round the clock face instead of the smaller one.

22.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.

23.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.

24.C — 4KA-0020Paper folding and hole punching

• AI forgot that the punch goes through every layer at once, not just the top one.
• BI undid only one of the two folds before counting the holes.
• DI doubled for the first fold and then added two more rather than doubling a second time.
• EI counted a fold that was never made, doubling three times instead of twice.

25.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.

26.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.

27.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.

28.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.

29.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.

30.B — 7KA-0157The pigeonhole principle

• AI thought that one more than the number of colours must give three of a kind, which only guarantees a PAIR.
• CI got to two of each colour, then added one more for each colour instead of one more in total.
• DI assumed the worst case meant emptying the largest pile of 12 reds first.
• EI answered with the number of socks I want rather than the number I must take to be sure of them.