AMC 10 · 2015 · #6
Grade 2 arithmeticPick an answer.
AMC 10 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Two days are already fixed, leaving only five open days for the three runs plus swimming and tennis. List the few legal ways to place the runs, then knock out the ones that force an illegal tennis day. One arrangement survives, and it pins down the swim day.
Fill in the fixed days
Monday is basketball, so golf falls two days later on Wednesday — leaving Tuesday and Thursday–Sunday open.
Nail down what you already know before guessing anything.
1.OA.A.1Draw A DiagramTuesday has to be a run
Four in-a-row days (Thu–Sun) hold at most two spaced runs, so the third run is forced onto Tuesday.
Four days in a row can only hold two spaced-out runs, so the third run is forced outside.
1.OA.A.1Eliminate PossibilitiesList the two remaining runs
The other two runs must stay spaced apart, giving only Thu & Sat, Thu & Sun, or Fri & Sun.
Only three spaced-out pairs fit in those four days, so just check all three.
2.OA.A.1Make A Systematic ListKnock out the bad run plans
Since tennis can't follow a run or a swim, only runs on Friday and Sunday survive; that forces tennis onto Thursday.
The tennis rule blocks every leftover day except when the swim lands on Saturday.
2.OA.A.1Eliminate PossibilitiesRead off the swim day
With runs Fri/Sun and tennis Thursday, the two open days leave the swim on Saturday — choice (E).
One arrangement survives every rule, and it puts the swim on Saturday.
1.OA.A.1Eliminate PossibilitiesLock in what you know, list the few legal options, then cross out the ones that break a rule.
- Fill in the fixed days
- Tuesday has to be a run
- List the two remaining runs
- Knock out the bad run plans
- Read off the swim day