Ordered half-search
Use higher/lower comparisons to exclude an entire half of an ordered range.
Adult planning suggestion: about6–9 · Logic & rule checking
- Players
- 2–3 per group
- Time
- 12–18 minutes
- Materials
- Numbered strip 1–16, hidden target slip and interval log.
Prepare
One learner secretly chooses an integer 1–16, writes it down and keeps the choice unchanged. Lay the sixteen possible values in increasing order. The seeker records lower and upper surviving limits, initially 1 and 16; a third learner audits honest feedback.
Play
Choose the lower middle integer of the surviving interval. Ask whether it equals the target. If not, the host says target higher or target lower. Cross out the tested number and the entire impossible side. Update limits before choosing another middle. The host compares values, not distance from the previous guess.
Worked example
For target 13: test 8, higher leaves 9–16; test 12, higher leaves 13–16; test 14, lower leaves 13–13; test 13 confirms equality. Guessing 14 after the feedback at 12 is legal even though the numerical distance to 13 is the same as 12: higher/lower is not hot-and-cold feedback.
Finish and check
End on equality or inconsistent feedback. If the interval becomes empty, unfold the committed target and repair the first wrong comparison rather than blame the seeker. With this midpoint rule, every target 1–16 is confirmed in at most five tests; sixteen is the five-test boundary example 8,12,14,15,16.
Adaptation and limits
For thirty learners use ten trios, rotating host, seeker and auditor. Use a finger or large marker on the strip and let an adult write. Compare the number of tests only for the same stated range and rule. The technical source describes binary search; this paper range and age planning are our adaptation.
Purpose, observation and provenance
Within this activity: Use higher/lower comparisons to exclude an entire half of an ordered range.
Ask which entire interval was ruled out and whether the target remains inside the surviving limits.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
CS Unplugged — Searching algorithms — Binary-search background; our 16-value game, five-test audit and age grouping are separate.
Age bands are planning suggestions. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Ordered half-search
Range 1–16; private target___; seeker must not see it.
Test / low / high / midpoint / higher,lower,equal.
Player record · keep host key separate
| Test | Low/high | Middle | Feedback |
|---|---|---|---|
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ |
Host key · separate from players
Target 13 tests 8,12,14,13. Target 16 uses 8,12,14,15,16. All sixteen targets take≤5 tests.
Run the round
One learner secretly chooses an integer 1–16, writes it down and keeps the choice unchanged. Lay the sixteen possible values in increasing order. The seeker records lower and upper surviving limits, initially 1 and 16; a third learner audits honest feedback.
Choose the lower middle integer of the surviving interval. Ask whether it equals the target. If not, the host says target higher or target lower. Cross out the tested number and the entire impossible side. Update limits before choosing another middle. The host compares values, not distance from the previous guess.
For target 13: test 8, higher leaves 9–16; test 12, higher leaves 13–16; test 14, lower leaves 13–13; test 13 confirms equality. Guessing 14 after the feedback at 12 is legal even though the numerical distance to 13 is the same as 12: higher/lower is not hot-and-cold feedback.
End on equality or inconsistent feedback. If the interval becomes empty, unfold the committed target and repair the first wrong comparison rather than blame the seeker. With this midpoint rule, every target 1–16 is confirmed in at most five tests; sixteen is the five-test boundary example 8,12,14,15,16.
For thirty learners use ten trios, rotating host, seeker and auditor. Use a finger or large marker on the strip and let an adult write. Compare the number of tests only for the same stated range and rule. The technical source describes binary search; this paper range and age planning are our adaptation.