fix(practice): check all later prefix sums for ambiguity, not just final answer

Previously, typing "3" for problem [2, 1, 30, 10, 1] with prefix sums
[2, 3, 33, 43, 44] would immediately show help for prefix sum 3 because
the code only checked if "3" was a digit-prefix of the final answer (44).

Now it correctly checks if "3" could be a digit-prefix of ANY later prefix
sum (33 in this case), making it ambiguous and allowing the user to continue
typing "33" to get help for that prefix instead.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/src/components/practice/hooks/__tests__/useInteractionPhase.test.ts

@@ -129,6 +129,18 @@ describe('findMatchedPrefixIndex', () => {
     expect(result.helpTermIndex).toBe(2) // help with term at index 2
   })
 
+  it('detects ambiguous match when prefix sum is digit-prefix of intermediate prefix sum', () => {
+    // Problem: [2, 1, 30, 10, 1] -> prefix sums [2, 3, 33, 43, 44]
+    // Typing "3" matches prefix sum 3 at index 1
+    // But "3" is also the first digit of "33" at index 2
+    // Note: "3" is NOT a prefix of "43" or "44" (those start with "4")
+    const multiSums = [2, 3, 33, 43, 44]
+    const result = findMatchedPrefixIndex('3', multiSums)
+    expect(result.matchedIndex).toBe(1) // matches prefix sum 3 at index 1
+    expect(result.isAmbiguous).toBe(true) // "3" is also digit-prefix of "33"
+    expect(result.helpTermIndex).toBe(2) // help with term at index 2
+  })
+
   it('returns no match for input that does not match any prefix sum', () => {
     const result = findMatchedPrefixIndex('5', sums)
     expect(result.matchedIndex).toBe(-1)

apps/web/src/components/practice/hooks/useInteractionPhase.ts

@@ -219,7 +219,7 @@ export interface PrefixMatchResult {
  * Finds which prefix sum the user's answer matches, if any.
  * Also detects ambiguous cases where the input could be either:
  * 1. An intermediate prefix sum (user is stuck)
- * 2. The first digit(s) of the final answer (user is still typing)
+ * 2. The first digit(s) of a later prefix sum (user is still typing)
  *
  * Leading zeros disambiguate and REQUEST help:
  * - "3" alone is ambiguous (could be prefix sum 3 OR first digit of 33)
@@ -241,7 +241,6 @@ export function findMatchedPrefixIndex(
   if (Number.isNaN(answerNum)) return noMatch
 
   const finalAnswer = prefixSums[prefixSums.length - 1]
-  const finalAnswerStr = finalAnswer.toString()
 
   // Check if this is the final answer
   if (answerNum === finalAnswer) {
@@ -265,12 +264,18 @@ export function findMatchedPrefixIndex(
     }
   }
 
-  // Check if user's input could be a digit-prefix of the final answer
-  const couldBeFinalAnswerPrefix = finalAnswerStr.startsWith(userAnswer)
+  // Check if user's input could be a digit-prefix of ANY later prefix sum
+  // For example, with prefix sums [2, 3, 33, 43, 44]:
+  // - "3" matches prefix sum at index 1, but could also be first digit of 33 or 43
+  // - So "3" is ambiguous
+  const couldBeLaterPrefixPrefix = prefixSums.slice(matchedIndex + 1).some((laterSum) => {
+    const laterSumStr = laterSum.toString()
+    return laterSumStr.startsWith(userAnswer)
+  })
 
   return {
     matchedIndex,
-    isAmbiguous: couldBeFinalAnswerPrefix,
+    isAmbiguous: couldBeLaterPrefixPrefix,
     helpTermIndex: matchedIndex + 1, // Help with the NEXT term after the matched sum
   }
 }