1.
A trader finishes his journey with 12 coins. At the last oasis he spent half of everything he had. Before that he found 8 coins. Before that he spent 5 coins on water. How many coins did he set out with? (Work backwards.)
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Answer:
Did you know? Across the Sahara, salt was once traded for gold by weight — salt kept food edible, and nothing else could.
2.
Camel loads are recorded as 3, 6, 5, 10, 9, 18, ___, ___. What are the next two? (Hint: two rules, taking turns.)
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Answer:
Did you know? A thirsty camel can drink over 100 litres in about ten minutes — roughly a full bathtub.
3.
Four oases lie along one road: Zahra, Rimal, Bahr, and Nakhl. Rimal is first. Nakhl is last. Bahr lies between Zahra and Nakhl. What is the order along the road?
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Answer:
Did you know? Camel humps store fat, not water. The fat is fuel, and burning it also releases a little water.
4.
A trader must cross a river with a goat, a sack of grain, and a jackal. The boat carries him and only one of them. Left alone together, the jackal eats the goat, and the goat eats the grain. How does he get all three across? Write the trips in order.
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Answer:
Did you know? Desert temperatures can swing more than 30 °C between afternoon and night — caravans often travelled after dark.
1.
You reach a fork. One road leads to the oasis, the other into the dunes. Two guides stand there: one always tells the truth, the other always lies — but you don't know which is which. You may ask one guide one question. What do you ask, and what do you do with the answer?
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Answer:
Did you know? Desert guides navigated by star, dune shape and wind direction — a route could be memorised for hundreds of kilometres.
2.
A merchant sells half his cloth, then sells 6 more bolts, then sells half of what is left, and finishes with 9 bolts. How many bolts did he start with?
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Answer:
Did you know? Caravans could run to several thousand camels, moving in a column many kilometres long.
3.
One caravan leaves every 9 days, another every 12 days. Both leave today. In how many days do they next leave together? How many times will that happen in a 365-day year?
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Answer:
Did you know? Timbuktu grew rich as the place where the desert caravan routes met the river trade going south.
4.
You have 9 sacks that look identical. One is heavier than the rest, which all weigh the same. Using a balance scale (no weights), what is the fewest weighings that always finds the heavy sack? Explain how.
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Answer:
Did you know? Merchants carried their own scales and standard weights, because a trusted weight was the only guard against a rigged one.
3rd Grade
1. 21 coins.
Run it in reverse and flip each step. Ended with 12 after halving → he had 24. Undo finding 8 → 16. Undo spending 5 → 21. Check forwards: 21 − 5 = 16, + 8 = 24, half spent = 12. ✓
2. 17 and 34. Double, then subtract 1, over and over.
3 ×2→ 6 −1→ 5 ×2→ 10 −1→ 9 ×2→ 18. Next is −1 = 17, then ×2 = 34.
3. Rimal, Zahra, Bahr, Nakhl.
Rimal 1st and Nakhl 4th leaves places 2 and 3 for Zahra and Bahr. Bahr must sit between Zahra and Nakhl, so Zahra is 2nd and Bahr 3rd.
4. 7 crossings — and the goat comes back.
Goat over → return empty → jackal over → bring the goat back → grain over → return empty → goat over. The move nobody thinks of is carrying something back.
4th Grade
1. Ask either guide: "If I asked the other guide which road leads to the oasis, what would he say?" Then take the other road.
Both possible guides give the same reply. Ask the truthful one and he honestly reports the liar's lie. Ask the liar and he lies about the truthful one's honest answer. Either way the road named is wrong, so you go the other way. One question does the work of two because it forces the answer through both guides.
2. 48 bolts.
Backwards, flipping each step: 9 is what's left after halving → 18. Undo selling 6 → 24. Undo the first halving → 48. Check: 48 → 24 → 18 → 9. ✓
3. Every 36 days; 10 times in a year.
Shared multiples of 9 and 12: 36, 72, 108... so every 36 days. Then 365 ÷ 36 = 10 remainder 5 → 10 times (not counting today).
4. 2 weighings.
Split into three groups of 3. Weigh 1: group A against group B. If one side sinks the heavy sack is there; if they balance it is in group C. Either way you now have 3 sacks. Weigh 2: one against another — if one sinks that's it, if they balance it's the third. Two weighings, always. Weighing them one at a time takes up to 8.