Motorola M500 Manuel d'utilisateur télécharger pdf (Page 28)

Page 26 M500 180

Letters to the Editors

Re: Problem 178.1 – Lottery guarantee.

Dear Tony,

With regard to the argument that 18424/20 tickets are required, this

is stated in the article in M500 161 to give twenty prizes of 10, thereby

implying that to guarantee one 10 prize a minimum of 922/20, say 47,

tickets are required. I think that 47 tickets is too small.

The probability of winning (only) the 10 prize is







56.6

This implies a minimum of 57 tickets would be required. However, the

probability of winning any prize (i.e. at least 10) is 1/53.6, so that 54

tickets are necessary. The great diﬃculty is how you actually select the

number in the correct combinations for the minimum number of tickets. I

have not been able to ﬁnd a systematic way of covering all 49 numbers with

only ﬁfty-something and I would be very interested to see how this can be

achieved whatever the minimum number of tickets is needed to guarantee a

win of at least 10.

The ‘expected value’ return per ticket is about 45p, so for every ticket

purchased at 1 there is an ‘expected loss’ of 55p. Even with a ‘clever

strategy’ which guarantees a 10 win it is diﬃcult to break even.

Yours sincerely,

Chris Pile

ADF—Problem 178.1 appears to be the subject of much research and,

as far as I am aware, the answer is not known. The current record holders

are Dragan Stojiljkovic and Rade Belic, who show that 163 National Lottery

tickets are suﬃcient to guarantee a 10 prize. Details of their plan can be

found in http://lottery.merseyworld.com/Wheel/Wheel.html.

Coincidence

Dear Jeremy,

The population of the country is about 50/60 million. Ten of them are

oﬃcers of the M500 committee. Three of them are my children. What is

the probability of one of my children selling his/her house to an oﬃcer on

the M500 committee?

The probability presumably depends a great deal on the ‘relation’ be-

tween myself and the committee members. That is we are/were all involved

with the OU.

A few years ago, my son, Jim, was living at 32 Lucas Place!

Colin Davies

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Motorola M500 Manuel d'utilisateur Page 28