Worksheet generator

1.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.

2.D — 30KA-0047Counting by position (sliding window)

• AI counted only the sixteen smallest squares and stopped there.
• BI counted the small squares and the single big one, and forgot every size in between.
• CI counted the 2 by 2 squares as four rather than nine, splitting the board into blocks.
• EI used 4 by 4 positions for every size instead of shrinking the range as the square grows.

3.C — 48KA-0070Counting with restrictions

• AI treated the twins as one child and forgot they can also swap places with each other.
• BI glued the twins together into a single block but then forgot that the block can be arranged with the others in more ways than I counted.
• DI halved the 120 total, assuming the twins are together in exactly half the arrangements.
• EI counted every arrangement of five children and forgot the twins' condition entirely.

4.E — 14KA-0133Counting shapes hidden inside a figure

• AI counted the nine small squares and stopped, missing every larger one.
• BI counted the small squares and the whole board, forgetting the middle size entirely.
• CI found the 2 by 2 squares by splitting the board into blocks, getting two instead of four.
• DI slid the 2 by 2 square across and down but missed one of its four positions.

5.A — 54KA-0177Overcount, then correct

• BI counted every line joining two vertices and forgot to remove the 12 sides.
• CI counted each diagonal from both of its endpoints and forgot to halve.
• DI used 12 x 10 without halving, double counting every diagonal.
• EI subtracted 24 rather than 12, removing each side twice.