Deduce #16: The allotment — the solution

The Deduce puzzle from August 30, 2026, worked through clue by clue: 8 clues, 4 rounds of crossing off, and no guessing anywhere.

The puzzle

Four people — Omar, Ben, Nadia and Marco — and three things to work out about each: their crop, tool and plot. The clues only ever rule things out.

1. Ben is the beans grower.
2. The beans grower is not the one on plot 3.
3. The one with the spade is on a lower plot than the carrots grower.
4. The onions grower is on a lower plot than Omar.
5. The one with the hoe is exactly 2 plots after the carrots grower.
6. Omar is not the rhubarb grower.
7. The one with the shears is the one on plot 3.
8. Marco is on a lower plot than the one with the shears.

The walkthrough

A round is one pass over the clues. Each round applies what the last one settled; every step below is an elimination the clues force, in the order a solver would take them.

Round 1

Start with every possibility open, and take the clues in order.

Clue 1, “Ben is the beans grower”: beans comes off Omar, Nadia and Marco. That settles it: Ben’s crop is beans.

Clue 2, “The beans grower is not the one on plot 3”: plot 3 comes off Ben.

Clue 4, “The onions grower is on a lower plot than Omar”: onions comes off Omar; plot 1 comes off Omar.

Clue 6, “Omar is not the rhubarb grower”: rhubarb comes off Omar. That settles it: Omar’s crop is carrots.

Clue 7, “The one with the shears is the one on plot 3”: shears comes off Ben.

Clue 8, “Marco is on a lower plot than the one with the shears”: shears comes off Marco; plot 4 comes off Marco.

Round 2

Go back over the clues with the new facts in hand.

Carrots is Omar’s, so it comes off Nadia and Marco.

Clue 3, “The one with the spade is on a lower plot than the carrots grower”: spade comes off Omar.

Clue 5, “The one with the hoe is exactly 2 plots after the carrots grower”: hoe comes off Omar and Marco; plot 3 and plot 4 come off Omar. That settles it: Omar is on plot 2.

Clue 7, “The one with the shears is the one on plot 3”: shears comes off Omar; plot 3 comes off Marco. That settles it: Omar’s tool is trowel, Nadia’s tool is shears and Nadia is on plot 3.

Round 3

Go back over the clues with the new facts in hand.

Trowel is Omar’s, so it comes off Ben and Marco. That settles it: Marco’s tool is spade.

Spade is Marco’s, so it comes off Ben. That settles it: Ben’s tool is hoe.

plot 2 is Omar’s, so it comes off Ben and Marco. That settles it: Marco is on plot 1.

plot 1 is Marco’s, so it comes off Ben. That settles it: Ben is on plot 4.

Clue 4, “The onions grower is on a lower plot than Omar”: onions comes off Nadia. That settles it: Nadia’s crop is rhubarb.

Round 4

Go back over the clues with the new facts in hand.

Rhubarb is Nadia’s, so it comes off Marco. That settles it: Marco’s crop is onions.

The answer

Previous: Deduce #15 (Sat, Aug 29) · Next: Deduce #17 (Mon, Aug 31)

About Deduce

Deduce is Noggin’s daily logic grid: four people, three things to work out about each, and clues that never hand you an answer. Every puzzle has exactly one solution and can be finished by crossing off alone. How to play Deduce, or play today’s.