1.
A lighthouse flashes in a repeating pattern: 1, 2, 4, 7, 11, ___, ___. What are the next two numbers, and what is the rule? (Hint: look at the gaps between them, not the numbers themselves.)
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Answer:
Did you know? Every lighthouse flashes its own pattern, called its character, so a sailor can tell which one they are looking at.
2.
There are 12 boats in the harbour. 7 have red sails. 6 carry a lantern. 3 boats have both. How many boats have neither a red sail nor a lantern?
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Answer:
Did you know? A lighthouse lens is built from rings of glass that bend scattered light into one straight beam, visible over 30 km away.
3.
Four lighthouses stand on the coast: Gull, Rock, Pine, and Sand. Gull is taller than Rock. Sand is the shortest of all. Pine is taller than Gull. List them from tallest to shortest.
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Answer:
Did you know? The Pharos of Alexandria, built over 2,000 years ago, was one of the seven wonders of the ancient world.
4.
On a balance, 1 big lamp exactly balances 3 small lamps. And 1 small lamp exactly balances 2 lenses. How many lenses would balance 1 big lamp?
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Answer:
Did you know? Keepers had to wind the clockwork that turned the lens by hand, sometimes every two hours, all night long.
1.
Three keepers are on duty and one of them forgot to light the lamp.
Idris says: "It wasn't me." Anas says: "It was Bilal." Bilal says: "Anas is lying."
Exactly one of the three is telling the truth. Who forgot?
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Answer:
Did you know? Before automation, a keeper's whole job was making sure the light never once went out between dusk and dawn.
2.
30 ships pass the lighthouse. 18 carry cargo, 14 carry passengers, and 5 carry both. How many ships carry neither?
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Answer:
Did you know? Lighthouses are painted in bold stripes or patterns so they can also be identified in daylight, when the lamp is useless.
3.
On a balance: 2 lenses and 1 lamp together weigh 11 kg. 1 lens and 1 lamp together weigh 7 kg. How much does one lens weigh? How much does one lamp weigh?
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Answer:
Did you know? A large Fresnel lens can weigh several tonnes yet float so freely on a bath of mercury that one hand can turn it.
4.
One lighthouse flashes every 4 seconds, another every 6 seconds. They flash together at exactly 12:00:00. How many seconds until they flash together again? How many times will they flash together in the first minute?
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Answer:
Did you know? Ships time a lighthouse's flashes with a stopwatch and look the rhythm up in a book to confirm exactly where they are.
3rd Grade
1. 16 and 22. The gaps grow by one each time.
Gaps are 1, 2, 3, 4 — so the next gaps are 5 and 6. 11 + 5 = 16, then 16 + 6 = 22.
2. 2 boats.
The 3 both-boats got counted twice, so boats with at least one = 7 + 6 − 3 = 10. Then 12 − 10 = 2. Drawing two overlapping circles makes this obvious.
3. Pine, Gull, Rock, Sand.
Pine > Gull and Gull > Rock chain together into Pine > Gull > Rock. Sand is shortest, so it goes last.
4. 6 lenses.
1 big = 3 small. Swap each small for 2 lenses: 3 × 2 = 6 lenses.
4th Grade
1. Idris forgot.
Test each. If Idris did it: his own claim is false, Anas is false, Bilal is true — exactly one truth. ✓ If Anas did it: Idris true and Bilal true — two. ✗ If Bilal did it: Idris true and Anas true — two. ✗ Only Idris fits.
2. 3 ships.
At least one = 18 + 14 − 5 = 27. Then 30 − 27 = 3. Subtracting the overlap once is the whole trick.
3. Lens 4 kg, lamp 3 kg.
The first weighing has exactly one extra lens and is 11 − 7 = 4 kg heavier, so a lens = 4 kg. Put it back: 4 + lamp = 7, so lamp = 3 kg.
4. Every 12 seconds; 5 times in the first minute.
Together on shared multiples of 4 and 6: 12, 24, 36, 48, 60. So every 12 seconds, and within 60 seconds that is 5 times (not counting the 12:00:00 start).