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Routes on a grid – practice for Years 5–9

Sample questions on Routes on a grid with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Logic
Year
Years 5–9
Curriculum area
Counting

Question types: Shortest routes

Rule: Routes on a grid

A shortest route goes only right and up. Routes to a crossing = routes to the crossing on its left + routes to the one below.

Routes through K: routes from A to K times routes from K to B. Routes avoiding K: all routes minus those through K.

Example: A 2 × 2 grid: 1 route to the top-left and bottom-right corners, 2 to the middle, 3 + 3 = 6 to B.

Watch out: Multiply the routes through K, don’t add them: 2 routes to K and 3 from K give 2 × 3 = 6 routes.

Sample questions

  1. Question 1 Easy

    The streets form a square grid. We walk from A to B by a shortest route, so only right and up. How many different routes are there?

    AB
    Show the solution
    Answer: 4

    How it works: The routes to each crossing are the routes to the crossing on its left plus the one below it: 4.

  2. Question 2 Normal

    The streets form a square grid. We walk from A to B by a shortest route, so only right and up. How many different routes are there?

    AB
    Show the solution
    Answer: 35

    How it works: The routes to each crossing are the routes to the crossing on its left plus the one below it: 35.

  3. Question 3 Hard

    The streets form a square grid. We walk from A to B by a shortest route, so only right and up. How many different routes pass through crossing K?

    ABK
    Show the solution
    Answer: 18

    How it works: There are 3 routes from A to K and 6 from K to B; any can join any: 18.

Related topics

All Logic topics

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