Worksheet generator

1.C — 5KA-0061Operation puzzles and cryptarithms

• AI solved for the triangle and gave that instead of the square.
• BI found the triangle is 4 and gave that number, without going on to the second equation.
• DI halved the 12 instead of dividing it by the three triangles.
• EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.

2.A — 1KA-0169Remainders and modular cycles

• BI reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.
• CI read the cycle backwards and landed on the entry before the right one.
• DI used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.
• EI assumed a power that large must be divisible by 5.

3.B — 15KA-0056Place value and digit positions

• AI checked that the digits differ and stopped, without working out how much the swap actually changes the number.
• CI saw a difference of 2 between the digits and expected that to give a change of 36.
• DI ignored the direction: swapping this number makes it smaller, not bigger.
• EI picked a number whose digits differ by 4 without noticing that the larger digit is already in front.

4.D — 2550KA-0058Clever regrouping (pair to round numbers)

• AI found the sum of 1 to 50 and forgot that every term here is twice as big.
• BI used 49 pairs instead of 25, losing one pair from the count.
• CI estimated the answer as a round number rather than pairing properly.
• EI paired the terms but forgot that pairing counts every number twice, so I never halved.

5.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.

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.D — 12KA-0060Operation puzzles and cryptarithms

• AI added the digits of 132 instead of working out what A and B must be.
• BI found A + B correctly and then halved it, as if the question wanted one digit.
• CI spotted the 11 in the working and gave that instead of the sum it multiplies.
• EI found a pair of digits by trial and misadded them by one.

9.C — 25KA-0135Digit-constraint puzzles

• AI counted the odd numbers in one row of ten and treated that as the whole answer.
• BI used four odd digits instead of five, forgetting that 9 is odd.
• DI counted every two-digit number that is itself odd, which only fixes the last digit.
• EI let the first digit be any of ten values rather than only the five odd ones.

10.B — 9KA-0158Last-digit behavior of products and powers

• AI used the first entry of the cycle because 2026 is even, without working out where in the cycle it lands.
• CI counted the cycle starting from zero, so a remainder of 2 put me one place too far along.
• DI assumed a power that large must end in 1.
• EI multiplied 3 by 2 and used the last digit of that.