Two question families that look different and are solved identically: family relationships, where the drawing is a tree, and direction sense, where the drawing is a compass map. In both, the sentences are instructions for drawing — and once the drawing exists, the answer is visible rather than deduced.
Both families are also traps for anyone who tries to hold them in their head. "A is the mother of B, B is the sister of C, C is the father of D" is four nodes and three edges when drawn, and a tangle of pronouns when not.
Relations: draw people as letters, connect them with labelled edges (parent, spouse, sibling), and mark gender wherever the question depends on it.
Directions: draw north as up, and treat every turn as a change of heading applied to the current one.
In both families, never answer from the sentence; answer from the drawing.
| Phrase | What it means |
|---|---|
| Only son of my grandfather | My father (if the grandfather is my father's father) |
| My father's brother | My uncle; his children are my cousins |
| My mother's brother's son | My cousin |
| Daughter of my father's sister | My cousin |
| Brother of my wife's father | My father-in-law's brother, not a blood relative of mine |
| Son of my grandfather's only daughter | My brother or me - the only daughter is my mother, so her son is my brother or me |
Two disciplines make relationship items reliable: write the gender on the node as soon as a word like mother, sister, son tells you, and read the path backwards as well as forwards, because many questions ask the relation in the opposite direction to the sentence.
If the person named could be either male or female, the correct answer is "uncle or aunt", "brother or sister". Questions designed this way test whether you noticed that the gender was never given; do not force a choice.
| Facing | Turn right | Turn left |
|---|---|---|
| North | East | West |
| East | South | North |
| South | West | East |
| West | North | South |
A half turn reverses the heading, and a full turn restores it. Shadow questions follow the sun: at sunrise a person's shadow points west, at sunset it points east, and at noon it is shortest and points north in the northern hemisphere.
Do not add up the legs of the walk. Add the north-south legs into one net displacement and the east-west legs into another, then use the right-angled triangle rule:
Draw it: Ali's grandfather has one son, who is Ali's father. The daughter of Ali's father is Ali's sister. The phrase "only son" exists to prevent you from considering an uncle's daughter.
Edges: A is a parent of B; B and C are siblings, so A is also a parent of C; C is a parent of D. Therefore A is D's grandmother — the gender came from the word "mother" two sentences earlier.
Q is S's mother (through R, S's father), and P is Q's brother, so P is S's maternal uncle.
Net displacement: 6 km south and 8 km east, a 6-8-10 triangle, so he is 10 km from the start. Adding the legs (14 km) is the trap.
X is the son of Y. Y is the sister of Z. How is Z related to X?
A man walks 5 km north, turns right and walks 3 km, turns right again and walks 5 km. How far is he from his starting point?
A man starts facing north, turns right twice and then turns left once. Which direction is he facing now?
At sunrise, a man standing in an open field has his shadow pointing:
Without looking back: how do you find the distance from the start, and what do you do when a person's gender is never given?
The answer: combine the north-south legs and the east-west legs separately and use the right-angled triangle rule; and answer "uncle or aunt" rather than forcing a choice.
To find the distance from the starting point, add the north-south legs into one net displacement and the east-west legs into another, then apply the rule. A right turn from facing east leads to . At sunset a shadow points . When the gender of a relative is never stated, the answer is uncle or .
"A woman walks 4 km north, then turns left and walks 3 km, then turns left again and walks 4 km. How far is she from the start, and in which direction?" Answer both, then explain what changes if the third leg is 6 km instead of 4 km.
Leg one: 4 km north. Facing north, a left turn gives west, so leg two is 3 km west. Facing west, a left turn gives south, so leg three is 4 km south. Net: the north and south legs cancel, leaving 3 km west of the start — she is 3 km from the start, to the west. Note that this is the same arithmetic as the earlier 5-3-5 walk; the pattern of three legs turning the same way always leaves you beside your starting point.
With the third leg at 6 km instead of 4 km, the net north-south becomes 4 − 6 = 2 km to the south, and the net east-west stays 3 km west. The distance becomes the hypotenuse of 2 and 3, which is the square root of 13, about 3.6 km, in the direction south-west of the start. The compass direction changed from west to south-west, which is why the question "how far" and the question "in what direction" must both be answered from the same net-displacement calculation.
Trees and maps are done. The next lesson is a small, entirely mechanical family that rewards pattern recognition rather than drawing: coding and decoding, where a letter or number transformation is stated once and applied to a new word.