Without a calculator, work out the cheapest route from Los Angeles to Las Vegas:

 LosAngeles 96 17 78 93 37 63 67 72 98 8 LasVegas

You can move from square to square horizontally or vertically (but not diagonally). Each time you enter a square you have to pay the amount shown.

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Topics: Starter | Arithmetic | Puzzles

• Richard Lewis, Chis & Sid GS
•
• I will be using this tomorrow with a bright Year 7 group. It's a great introduction to real-world logistics problems!
However it strikes me that increasing the size of the numbers in the grid doesn't actually significantly increase the complexity because it is still relatively easy to spot the smaller and larger value routes on such a small grid.
Adding another row to the grid would possibly be a better way of raising the difficulty level since there are then more options to evaluate mentally.
• Callum - Year 6, Charnwood Primary - Lichfield
•
• I found this starter very easy, perhaps more numbers or higher numbers would make it more challenging.
• Transum,
•
• Thank you Richard, Chris, Sid and Callum for your feedback. Buttons can now be found lower down the page to produce the grids you suggested.

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## Answers

There are 10 different five step routes from Los Angeles to Las Vegas.

Los Angeles - 96 - 17 - 78 - 67 - Las Vegas [Total = 258]

Los Angeles - 96 - 17 - 63 - 67 - Las Vegas [Total = 243]

Los Angeles - 96 - 17 - 63 - 8 - Las Vegas [Total = 184]

Los Angeles - 96 - 37 - 63 - 67 - Las Vegas [Total = 263]

Los Angeles - 96 - 37 - 63 - 8 - Las Vegas [Total = 204]

Los Angeles - 96 - 37 - 98 - 8 - Las Vegas [Total = 239]

Los Angeles - 93 - 37 - 63 - 67 - Las Vegas [Total = 260]

Los Angeles - 93 - 37 - 63 - 8 - Las Vegas [Total = 201]

Los Angeles - 93 - 37 - 98 - 8 - Las Vegas [Total = 236]

Los Angeles - 93 - 72 - 98 - 8 - Las Vegas [Total = 271]

So the cheapest route costs 184 (dollars). Here is a way of getting that total:

 LosAngeles 96 17 78 93 37 63 67 72 98 8 LasVegas

You can view another version of this starter generated from random numbers. Puzzle 1 is the easiest, puzzle 5 is very difficult.

Alternatively you can change the size of the grid to make the problem more complex:

Number of rows: Number of columns:

Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter from random numbers.

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