Concepts · Word order

Dictionary order

The first letter that differs decides. Unless one word runs out.

Riya has to put these in dictionary order:

CART, CAR, CARE, CARPET, CARD

All five start CAR, so she compares the fourth letters: T, nothing, E, P, D. CAR has no fourth letter at all. She puts it at the end, where missing things usually go, and is not sure.

Your phone already knows

That evening she rings her cousin Raj. He is at the top of the R’s in her contacts: Raj, then Rajani, then Rajiv, then Ram.

Why is Raj first? Because it is the shortest, she thinks. Then she sees Ram, just as short, sitting below Rajiv.

So length is not it, she realises. R, A, J match in Raj, Rajani and Rajiv, and Raj stops there: it runs out first, and running out counts as coming first. Ram matches only R and A, then M meets J, and J comes first. A phone sorts names the way a dictionary sorts words, and Riya has been reading that list every day without noticing the rule. She takes out the question paper and moves CAR from the bottom of her list to the top.

The rule

Compare two words from the left, one letter at a time. The first letter where they differ decides, and nothing after it counts. If every letter matches until one word runs out, that word comes first.

Cross out the shared start. Compare what is left; an empty leftover goes first.

Riya’s list, again

  1. All five share CAR. Cross it out. What is left: T, nothing, E, PET, D.
  2. Nothing goes first, so CAR. Then D, E, P, T: CARD, CARE, CARPET, CART.
  3. The order is CAR, CARD, CARE, CARPET, CART.

CARPET has six letters and still comes before CART. Length by itself decides nothing: the first difference does, and running out counts as one.

When the tie runs long

MARBLE or MARCH? M, A and R match. Then B against C, and B comes first, so MARBLE wins, whatever follows. The L and the E never get a vote.

Why it helps in the paper

When the words share a long beginning, the deciding letter can be the fourth or the fifth, and one word may be the start of another. One habit settles all of it: write the shared start once, cross it out, and sort only what is left.

Try three

1. Which of these words comes first in a dictionary?

  1. PENCIL
  2. PENNY
  3. PENGUIN
  4. PENALTY
Hint

All four start PEN. Look only at the fourth letter.

Answer

PENALTY

PEN is shared, so cross it out. The fourth letters are C, N, G and A.

A comes first, so PENALTY comes first.

2. Arrange these words in dictionary order: 1. Ball 2. Balloon 3. Bale 4. Bald

  1. 3, 4, 1, 2
  2. 4, 3, 1, 2
  3. 4, 3, 2, 1
  4. 1, 2, 4, 3
Hint

Cross out BAL. One of the words is the start of another.

Answer

4, 3, 1, 2

After BAL the leftovers are L, LOON, E and D.

D before E before L: Bald, Bale, Ball. Ball and Balloon tie on BALL, and Ball runs out first, so it comes first.

Bald, Bale, Ball, Balloon: 4, 3, 1, 2.

3. Put these in dictionary order: 1. Stamp 2. Star 3. Stand 4. Start 5. Stack. Which word comes third?

  1. Stamp
  2. Stand
  3. Star
  4. Start
Hint

All five start STA. Sort by the fourth letter, and look further only where two of them tie.

Answer

Stand

After STA the fourth letters are M, R, N, R and C. So Stack (C), Stamp (M), Stand (N), and then the two R words.

Star and Start tie on STAR, and Star runs out first. The order is Stack, Stamp, Stand, Star, Start. The third word is Stand.

Next mock

A week later: SING, SINK, SIN, SINGER Riya crosses out SIN. What is left: G, K, nothing, GER. Nothing first. G and GER tie on G, and G runs out first. Then K. She writes SIN, SING, SINGER, SINK.

The app has fifteen reasoning topics, and every question there is answered before its solution shows.

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