SUNDAY TIMES TEASER 2499

[NIMROD]

Is anyone able to explain to me the interpretation of Teaser 2499 (15 August ) Sunday Times?
It's about stocking shelves in a supermarket with milk and I can't understand the wording. For example, when it says 'half that amount the next day', are the old litres of milk sold as well? And when it says 'half that new amount the next day' what new amount is being referred to? I would appreciate any help!

[squarebear]

Care to post the exact question instead of just snippets?

[NIMROD]

I'm so pleased someone has responded, Squarebear- here is the complete Teaser!

Joe was talking to the supermarket manager about shelf stocking, and she mentioned a recent exercise with milk.
Each morning, they added sufficient new stock to ensure there were 1,200 litres on the shelves. They found that 56% of the new stock was sold on the first day, half that amount the next day and half that new amount the day after. Any remaining stock was regarded as out of date and removed next morning before restocking.
Hence, they calculated the number of litres to be added each morning.

What is that number?

I send in the Teaser solution most weeks but this one really has me wondering!
Hope to hear your comments!

[Dinkypuzzled]

I believe it only refers to the original 1200 litres.
56 per cent on day 1 = 1200 x 56 per cent = 672
half that on day 2 = 672 / 2 = 336
half that on day 3 = 336 / 2 = 168
(so order 528 + 336 + 168 litres) = 1176 litres. (24 being 'out of date')

[NIMROD]

Thanks for your response Dinkypuzzled but I am still very puzzled!
528 is the number unsold on the first day - is that what you mean?
The total of 1176 is the total of the new (each day) litres unsold.
I seem to have a blind spot as far as this Teaser is concerned!

[Dinkypuzzled]

Sorry, Nimrod. I have had a rethink. Over the three days, 1176 were sold. Divide that by three makes 392. If 392 were bought each day, then there would be sufficient - and none of the 24 would need to be removed. Any good ?

[NIMROD]

Thanks for your latest response Dinkypuzzled! Yesterday I was so annoyed with this teaser that I searched for 'Teaser 2499' and, lo and behold, found a site where a group of very bright types were discussing the problem! I found Guy's reasoning intelligible but Garry's too tricky for my simple logic! Anyway, it gave me some insight into the problem which, I think, was so badly explained in the Sunday times in the first place. Perhaps you would like to have a look -

http://groups.google....imes-teaser-solutions
Good luck!

[Dinkypuzzled]

I looked.
I'll not spend any more time on it - but perhaps you could let me know the answer (if it is published) on this thread after Sunday.
Cheers !

[NIMROD]

Will do, Dinkypuzzled - but the answer won't be published until a week on Sunday.

[dundurn]

Every day you replenish 750l

You sell 420l on day 1, 210l on day 2 and 105; on day 3. The remaining 15l you discard. Your daily stock is made up of 750l of fresh milk, 330l (750 -420) unsold from the fresh stock the previous day and 120l (750 -420 -210)unsold from 2 days ago. 750 +330 +120 = 1200

[dundurn]

I initially calculated this by using an iterative process - starting on the very first day of sales with a 1200l replenishment figure and then wotking forwards day by day until the series converged on 750l. In retrospect the solution is much simpler - straight algebra.
Imagine it's Thursday. All of the milk that was put on the shelves fresh on Monday was either sold on Monday, sold on Tuesday or sold or discarded on Wednesday. You Thursday morning stock of 1200l is therefore made up of X litres, being your restock amount, plus 44% of X, being the unsold milk from Wednesday's restock plus 16% of X, being the unsold milk from Tuesday's restock. So X + 0.44X +0.16X = 1200l i.e.1.6X = 1200l, so X = 750l

[NIMROD]

As you can see from dundurn's very clear explanation, the answer to the Teaser was 750l, Dinkypuzzled. I hadn't looked at this thread since 19th Aug - thanks to both of you for the correspondence and interest!

[Dinkypuzzled]

Ah !
(I'm glad I only teach Primary School pupils.)