1.
Four rivers — W, X, Y, and Z — were measured. W is longer than X. Y is shorter than X. Z is longer than W. List all four from longest to shortest.
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2.
Three captains — Nadia, Yusra, and Tariq — each pilot one boat: a ferry, a barge, or a canoe. Nadia does not pilot the canoe. Tariq pilots the barge. Who pilots each boat?
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3.
At 1:00 a river gauge reads 5 cm. Rain makes the reading double every 15 minutes. What does the gauge read at 2:00?
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4.
Stepping stones are numbered 1 to 30. Every 3rd stone is mossy. Every 5th stone is painted. Which stones are both mossy and painted? And how many stones have neither?
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1.
Five rivers were ranked by how fast they flow. The Blue flows faster than the Grey. The Green flows slower than the Grey. The Silver flows faster than the Blue. The Amber flows somewhere between the Green and the Grey. List all five from fastest to slowest.
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2.
A guide says: “Every boat we launched on Friday was a kayak.” On Saturday she launches a kayak. Does that prove her statement was right? Explain what her statement does and does not tell you.
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3.
A barge leaves a dock at 7:20 in the morning and travels for 6 hours and 50 minutes. It arrives where the clocks are 1 hour ahead of the dock. What time is it on the local clock when the barge arrives?
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4.
Buoys stand along a 240 km river channel, one every 40 km, with a buoy at the very start and one at the very end. How many buoys are there in total?
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5.
5 river-survey teams meet at a landing. Every team shakes hands with every other team exactly once. How many handshakes happen altogether?
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Answer:
3rd Grade
1. Z, W, X, Y.
W > X and Y < X puts them W, X, Y. Z > W goes on the front: Z, W, X, Y. Build the chain one clue at a time instead of guessing.
2. Tariq — barge. Nadia — ferry. Yusra — canoe.
Tariq is given. Nadia is not the canoe and the barge is taken, so Nadia has the ferry. Yusra gets what is left. The “not” clue does the work.
3. 80 cm.
1:00 → 2:00 is 60 minutes = four 15-minute steps. 5 → 10 → 20 → 40 → 80. Counting the doublings is the puzzle; 5 × 4 = 20 is the trap.
Both: stones 15 and 30. Neither: 16 stones.
Both = multiples of 15 → 15 and 30. Mossy (3, 6, 9…) = 10 stones, painted (5, 10, 15…) = 6, minus the 2 counted twice = 14 tagged, so 30 − 14 = 16 with neither.
4th Grade
1. Silver, Blue, Grey, Amber, Green.
Silver > Blue > Grey from the first and third clues; Green is below the Grey; the Amber sits between Green and Grey. The “between” clue only makes sense once the others are placed.
2. No — it proves nothing about Saturday.
Her statement is only about Friday's boats. A kayak on Saturday is neither proof nor disproof. The one thing that would disprove her: a Friday boat that was not a kayak. Accept any answer that separates “all Friday's were kayaks” from “every kayak is launched on Friday”.
3. 3:10 in the afternoon (15:10) local time.
7:20 + 6 h = 1:20 pm, + 50 min = 2:10 pm dock time. Local clocks are 1 hour ahead, so 3:10 pm. Do the elapsed time first, adjust the zone second.
4. 7 buoys.
240 ÷ 40 = 6 gaps, and buoys at both ends means 6 + 1 = 7. The classic fencepost error: 6 is the number of gaps, not buoys.
5. 10 handshakes.
Each of the 5 teams shakes 4 others = 20, but every handshake was counted from both sides, so 20 ÷ 2 = 10. Or add 4 + 3 + 2 + 1.