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Probability and sequence

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5. If Kate starts on the paving stone outside her house and hops onto every second stone, she will get to the second to last stone before the house of her friend Sam.

(see diagram)

If Kate now turns round on this stone and hops onto every third stone, she will get back to the third stone.

(see diagram)

Kate turns back on the third stone and now jumps onto every fifth stone. She finished on the last stone outside Sam's house
(see diagram)

(i) Explain why the number or paving stones between the two houses
(a) is an even number
(b) is not a multiple of 3

(ii) Find the number of paving stone between the houses.
(ii) How many paving stones does Kate not land on during the game?

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Solution Summary

Probability and sequence skills are demonstrated. The number or paving stones between the two houses are explained.

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Solution:

This shows that Kate is always landing on an odd numbered stone. After the final step, one stone is reported to be left. So, the number of steps should be even.

In this trip Kate lands on those stones, which have multiples of 3 as their serial number. So, the stone from where Kate started back should have the serial number that is a multiple of 3. As Kate started from a stone that is second from last, total number of stones is of the form 3k+1 and hence the total number ...

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