Types
- Comparison: heights, weights, marks, ages or money of 5-8 persons; find who is 3rd tallest, how many are heavier than X, or a possible value.
- Position in a row / rank in a class: "Ravi is 14th from the top and 23rd from the bottom" (the site generates these).
- Comparison with values: "the second heaviest weighs 68 kg"; then "which can be the weight of A?"
Rank formulas
| Given | Result |
|---|---|
| Rank from top = a, from bottom = b | Total = a + b - 1 |
| Total N, rank from top = a | Rank from bottom = N - a + 1 |
| A is a-th from left, B is b-th from right, no overlap | Persons between = N - a - b |
Method for comparison puzzles
- Write each clue as a chain using > (taller/heavier/older): "P is heavier than Q but lighter than S" becomes S > P > Q.
- Join chains through common persons into one vertical list.
- Fix exact positions from "only" clues: "C is heavier than only two persons" means C is third from the bottom.
- Where two persons are not compared, keep them on the same level with a bracket - do not guess an order.
- For value questions, the unknown weight lies strictly between its neighbours' values.
Worked example
Six friends: C is taller than A and D; B is shorter than D; E is taller than C but shorter than F. Chain: F > E > C, and below C we have A and D with D > B. A is not compared with D or B, so the bottom three can be A-D-B, D-A-B or D-B-A. The third tallest is definitely C, but the third shortest can be A or D.
Interchange questions
"A is 10th from the left and B is 15th from the right. When they interchange positions, A becomes 20th from the left." A's new position is B's old position, so B's old position from the left is 20. Total = 20 + 15 - 1 = 34. Always convert both people's positions to the same end before adding or subtracting.
Trap: "taller than only two" is not "taller than two". "Only" fixes the exact number. Also, if a question asks "who can be", choose the option that covers every valid case.
Time target
45-75 seconds for a single comparison question; rank formulas 20 seconds.