Worksheet generator

1.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.

2.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.

3.A — 8KA-0144Translating a sentence into an equation

• BI subtracted 8 from 19 rather than working the two steps backwards.
• CI subtracted the 3 from 19 and gave that without halving it.
• DI added the 3 to 19 instead of subtracting it.
• EI doubled 19 and added 3, applying the machine forwards instead of undoing it.

4.D — 24KA-0073Arrangements of a few objects

• AI counted the letters rather than their arrangements.
• BI multiplied 4 by 3 and stopped, forgetting the last two positions.
• CI used 4 choices for every position, as if letters could repeat.
• EI used 4 choices in each of four positions, which allows every letter to repeat.

5.E — 408KA-0129Sanity-check with a second method

• AI worked out 17 times 20 and forgot to add the 17 times 4 part.
• BI worked out 17 times 4 as 28 instead of 68 when adding the parts together.
• CI worked out 17 times 4 as 48 instead of 68 when adding the parts together.
• DI made a carrying slip of ten in the final addition of the two parts.

6.E — 9KA-0037Last-digit behavior of products and powers

• AI assumed a number this large has no reachable last digit and gave up on the cycle.
• BI found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.
• CI found the cycle but counted its positions starting at zero, shifting my answer along by one.
• DI assumed the units digit of any power of 7 is always 7.

7.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.

8.B — 10KA-0082Shortest paths on and around shapes

• AI measured the straight line through the middle of the room, but the ant has to stay on the surfaces.
• CI unfolded the room but folded out the short wall rather than the one that makes the shortest route.
• DI chose an unfolding that gives a longer straight line and did not compare it with the others.
• EI walked along the edges of the room, 8 then 4 then 2, instead of cutting straight across the surfaces.

9.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.

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.