Reasoning · Grade 2-2 Tables and Graphs

Problem

Solve a table from given clues

A table holds grades 1-6, with grade 1 = 3, grade 4 = 6 and the total 33 given. Grade 2 is one fewer than grade 4 and grade 5 one more. Grade 1 must be strictly fewest and grade 6 strictly most. Fill in grades 2, 3, 5 and 6.
Your answer
How to solve
Strategy Guess and Check — Two clues give grades 2 and 5 directly from grade 4. That leaves only grades 3 and 6, whose sum I get by working backwards from the Total. With that single sum fixed, I guess-and-check the few possible (grade 3, grade 6) pairs and keep the one where grade 1 stays the fewest and grade 6 is the most.
1STEP 1

Fill grades 2 and 5 from grade 4

From grade 4 = 6 come grade 2 = 5 and grade 5 = 7.

6 - 1 = 5, 6 + 1 = 7
2STEP 2

Work backwards from the Total to get grade 3 + grade 6

The four known make 21, so the last two sum to 12.

3 + 5 + 6 + 7 = 21, 33 - 21 = 12
3STEP 3

Guess-and-check the (grade 3, grade 6) pair

Grade 6 needs 8+ and grade 3 needs 4+, leaving only grade 3 = 4, grade 6 = 8.

4 + 8 = 12
Answer
grade 2 = 5, grade 3 = 4, grade 5 = 7, grade 6 = 8
Adding the completed row, 3 + 5 + 4 + 6 + 7 + 8 = 33, matches the given Total. Grade 1 (3) is strictly the smallest and grade 6 (8) is strictly the largest, grade 2 (5) is one fewer than grade 4 (6), and grade 5 (7) is one more - every clue holds.
Takeaway

Pin the cells the clues hand you, subtract from the total to find what's left, then check the few splits against 'fewest' and 'most' - only one table fits!

  • Fill grades 2 and 5 from grade 4
  • Work backwards from the Total to get grade 3 + grade 6
  • Guess-and-check the (grade 3, grade 6) pair