#### wubie

Hello,

I am currently taking a course which has exercises/questions whose solutions are based on discrete mathematics. For anyone interested, the link to the course is:

http://www.math.ualberta.ca/~tlewis/222_03f/222_03f.html [Broken]

We are encouraged to discuss these problems with others since some of the problems can be very challenging. Solutions then may be submitted jointly (or individually as long as credit is given where credit is due).

I have not been able to find anyone with whom to collaborate. So I post my questions here in hopes to collaborate with those in the forum that like challenging questions. Here is a question under the section of modular arithmetic:

The inspectors of fair trading found that a wholesaler of golfing equipment was swindling his retailers by including one box of substandard golf balls to every nine boxes of top grade balls he sold them. Each box contained 6 golf balls, and the external appearance of all the balls was identical. However, the substandard balls were each 1 gram too light. The retailers were informed of this discrepancy. The boxes all arrived in packs of ten, each with one substandard box - but which one?

Phoebe Fivewood, the professional at a prestigious golf course, had just taken delivery of a large order so needed to sort them out quickly. She soon found a way to do this using a pair of scales (not pan balances) which required only one weighing on each scale for each batch of ten boxes. How did she do it? Note that she did not need to know what a golf ball should weigh.

I am not sure how "Phoebe Fivewood" figured this out. I have done similar question relating to coins in which pan balances were used but the solution or possible solutions to this question are eluding me.

Any thoughts on how to approach this question would be appreciated.

Cheers.

wubie.

I am currently taking a course which has exercises/questions whose solutions are based on discrete mathematics. For anyone interested, the link to the course is:

http://www.math.ualberta.ca/~tlewis/222_03f/222_03f.html [Broken]

We are encouraged to discuss these problems with others since some of the problems can be very challenging. Solutions then may be submitted jointly (or individually as long as credit is given where credit is due).

I have not been able to find anyone with whom to collaborate. So I post my questions here in hopes to collaborate with those in the forum that like challenging questions. Here is a question under the section of modular arithmetic:

The inspectors of fair trading found that a wholesaler of golfing equipment was swindling his retailers by including one box of substandard golf balls to every nine boxes of top grade balls he sold them. Each box contained 6 golf balls, and the external appearance of all the balls was identical. However, the substandard balls were each 1 gram too light. The retailers were informed of this discrepancy. The boxes all arrived in packs of ten, each with one substandard box - but which one?

Phoebe Fivewood, the professional at a prestigious golf course, had just taken delivery of a large order so needed to sort them out quickly. She soon found a way to do this using a pair of scales (not pan balances) which required only one weighing on each scale for each batch of ten boxes. How did she do it? Note that she did not need to know what a golf ball should weigh.

I am not sure how "Phoebe Fivewood" figured this out. I have done similar question relating to coins in which pan balances were used but the solution or possible solutions to this question are eluding me.

Any thoughts on how to approach this question would be appreciated.

Cheers.

wubie.

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