Page 9-47, Question 8

[Blueballoon5%]

In this question, isn't possible that some of the charities have no toys? It doesn't have the usual phrasing of "Each charity is assigned at least one toy."

[Jon Denning]

Hi blue - thanks for the question! I've got this drill question on page 9-60 in my copy of the book (which is likely more recent), so just FYI for anyone else who happens to read this

As to whether it's possible that a charity receives no toys, I would say no from the scenario ("toys are given to four charities" to me implies that each receives at least one), and certainly once we explore the rules a bit it becomes impossible for any charity to have zero: charity 2 has at least one, charity 3 has more than charity 2 (so at least two), and charity 4 is one less than charity 3 (so charity 4 gets a minimum of one). And of course charity 1 gets three times as many as charity 2, so charity 1 gets at least three toys.

Without those rules if I was still uncertain about a zero-toy option I'd quickly glance at the questions and answers and see if the situation ever arises. If it's shown as possible in a question or answer choice then you know it's allowed, and if it doesn't ever come up then chances are it's not possible (or at least won't matter).

I hope that helps!

[Blueballoon5%]

Thanks Jon!

[TargTru99^]

Greetings,

I got all of the correct distributions as my answers except for the 6-2-3-2, which was in the answer key. I had been thinking that since the number of toys given to the 4 charities were unknown, there could be an infinite number of toys being given, which Is why I believe I did not get 6-2-3-2 as one of my answers. Can explain to me how the finite 6-2-3-2 distribution is possible?

[Erik Christensen]

Targtru,

It is true that the overall number of toys given is unknown, however, there is an upper constraint by virtue of the fact that Charity 4 is given at most two toys. This sets an upper limit on the overall number of toys given to all of the charities because the number of toys given to each charity is linked to how many toys given Charity 4 either directly through the second rule or indirectly through a combination of rules.

Let's look at the 6-2-3-2 distribution to make sure it satisfies all of the rules.

Rule #1: Charity 1 is given three times as many toys as Charity 2. YES, SATISFIED. 6 for #1 is three times 2 for #2.

Rule #2: Charity 3 is given one more toy than Charity 4. YES, SATISFIED. 3 for #3 is one more than 2 for #4.

Rule #3: Charity 2 is given at least one toy. YES SATISFIED. 2 toys for #2 (at least one condition is satisfied because 2 is greater than 1).

Rule #4: Charity 4 is given at most two toys. YES SATISFIED. 2 toys for #4.

When identifying potential numerical distribution sets, make sure you identify all of the relative constraints at the upper and lower end for each variable, and then test all of the various options within those constraints so you are able to identify every distribution possible.

Let us know if you have any more questions!!

ERIK