units-digit-tracking
Determine the last digit of a multi-digit arithmetic expression by tracking only the units digit through additions and subtractions. Exploits that the ones column is closed under mod 10, so the bulk of the digits can be ignored.
How to solve
- Swap repeated_digit from 2 to 7 — units digit pattern shifts but strategy is identical
- Mix in one addition among the subtractions to force students to track sign carefully
- For an easier Grade-3 variant use addition only with 3-digit operands
Sub-archetype mix (3)
Click a row to see member problems.
- power-cycle-lookup 40% (6)
Find the units digit of a base raised to a large exponent (possibly added to other such terms). Reduce the base to its units digit, compute the first few powers to expose a short repeating cycle (length 1, 2, or 4), then index into that cycle using the exponent mod cycle length.
- tail-collapses-to-zero 27% (4)
A long sum or product chain where, past some index, every term has units digit 0 because a factor of 10 (or a 2-and-5 pair) appears in its construction. Compute the first few terms, notice where the units digit goes to 0 forever, discard the tail, and sum the finite prefix mod 10.
- digitwise-additive-reduction 33% (5)
A multi-term expression built only from addition and subtraction of specific concrete numbers (no exponents, no recursion). Replace each term with just its units digit, then add or subtract those single-digit values mod 10 to read off the answer.
More data (year-over-year, tool fingerprint, grade distribution, all members)
Tool fingerprint (1–17)
Grade distribution
- Gr 4 4
- Gr 5 3
- Gr 6 1
- Gr 7 2
- Gr 8 3