1. The matchsticks. Using six matchsticks of equal length, make four equilateral triangles. You may not break or bend any stick.
2. The missing rupee. Three friends pay 300 rupees for a room, 100 each. The manager realises the room costs 250 and sends 50 back with a boy. The boy keeps 20 and returns 10 to each friend. So each friend paid 90, totalling 270. The boy has 20. That makes 290. Where is the missing 10 rupees?
3. The two jars. You have a 5-litre jar and a 3-litre jar, and a tap. Measure exactly 4 litres.
4. The sequence. What comes next? 1, 11, 21, 1211, 111221, …
Answers.
1. Stop working flat. Build a tetrahedron — a three-sided pyramid. Six edges, four triangular faces.
2. There is no missing rupee; the question adds the wrong things. The friends paid 270. Of that, 250 went to the room and 20 to the boy. 250 + 20 = 270. Adding the boy’s 20 to the 270 double-counts it.
3. Fill the 5. Pour into the 3, leaving 2 in the big jar. Empty the 3. Move the 2 litres into it. Fill the 5 again and top up the 3-litre jar, which takes just 1 litre. Exactly 4 remain.
4. 312211. Each line describes the one above it out loud: “one one”, “two ones”, “one two, one one”. The previous line reads as three ones, two twos, one one.
