# Conference Topics Puzzle

Tom and four others spoke at a recent astrophysics conference, each presenting a paper on a different topic. Can you find the order in which the five talks were given, the full name of each speaker (one was Mr. Jones), his or her topic, and the number of people who attended each presentation?

1. The first talk of the day was on the big bang theory.

2. Laura drew 24 listeners, more than any other speaker

3. No two men spoke consecutively.

4. As many people attended the talk on pulsars as attended both the third speech and Gray's talk combined.

5. Howe's talk was attended by twice as many people as Ed's.

6. The last two speakers drew (not necessarily respectively) the largest and smallest numbers of attendees.

7. The talk about black holes drew half as many listeners as the second speech.

8. The talk on stellar evolution (which wasn't the one given by Christa Flynn) didn't draw the fewest attendees of the day.

9. The number of people who attended Samuel's talk was as much less than the number who attended the talk on quasars as it was more than the number who attended Ives's talk.

10. A different number of people attended each talk.

Source: mysterymaster

I think I have determined the order of the topics (big bang-quasars-stellar-pulsars-black holes) but am not being able to determine the gender and surnames.Also what is the best approach towards solving these kind of puzzles (using/without using grids)?

## 1 Answer

There're a few bits that can be done before drawing up a grid (and are probably required in order to do so):

Point 3 tells us that no two men spoke consecutively. There are 3 male first names (Tom, Ed, Samuel) and 2 female first names (Laura, Christa), so that tells us that the order of speakers by gender is mfmfm. (note: some assumptions made regarding names and genders)

Starting to fill in a grid:

Points 2 and 6 tell us that Laura had the most listeners and that one of the last two speakers had the most listeners, so Laura was second last. This also tells us that Christa Flynn was second. We also know that the first talk was on the big bang theory

$$\begin{array}{|c|c|}\hline\text{ TALK NUMBER }&\text{ 1 }&\text{ 2 }&\text{ 3 }&\text{ 4 }&\text{ 5 }\\ \hline \text{ FIRST NAME }&\text{ 1 }&\text{ Christa }&\text{ 3 }&\text{ Laura }&\text{ 5 }\\ \hline \text{ SURNAME }&\text{ 1 }&\text{ Flynn }&\text{ 3 }&\text{ 4 }&\text{ 5 }\\ \hline \text{ TOPIC }&\text{ BBT }&\text{ 2 }&\text{ 3 }&\text{ 4 }&\text{ 5 }\\ \hline \text{ LISTENERS }&\text{ 1 }&\text{ 2 }&\text{ 3 }&\text{ 24 }&\text{ few }\\\hline \end{array}$$

Stellar evolution wasn't Christa's talk, nor was it the least attended, so it's not the 1st, 2nd, or last talk. Black holes had half as many listeners as speech 2, so it can't be speech 4 (since that's the most attended). Pulsars is not the least attended (nor speech 3), since it's described as a sum of two others. We're also told more people attended the quasar talk than attended Samuel's. This puts black holes as the least attended, and thus speech 5.

$$\begin{array}{|c|c|}\hline\text{ TALK NUMBER }&\text{ 1 }&\text{ 2 }&\text{ 3 }&\text{ 4 }&\text{ 5 }\\ \hline \text{ FIRST NAME }&\text{ 1 }&\text{ Christa }&\text{ 3 }&\text{ Laura }&\text{ 5 }\\ \hline \text{ SURNAME }&\text{ 1 }&\text{ Flynn }&\text{ 3 }&\text{ 4 }&\text{ 5 }\\ \hline \text{ TOPIC }&\text{ BBT }&\text{ P?/Q? }&\text{ SE?/Q? }&\text{ P?/SE?/Q? }&\text{ BH }\\ \hline \text{ LISTENERS }&\text{ 1 }&\text{ few*2 }&\text{ 3 }&\text{ 24 }&\text{ few }\\\hline \end{array}$$

Laura is not Jones (Mr.), Gray (point 4 says Gray didn't have the most listeners), or Ives (point 9, fewer listeners than Samuel). This makes her Howe. Per point 5, Ed had 12 listeners. Per point 7, we can infer that the BH talk had fewer than 12 listeners, and so Ed did not present it. From point 9, Samuel is either Gray or Jones, and also did not present the BH talk (so Tom did).

$$\begin{array}{|c|c|}\hline\text{ TALK NUMBER }&\text{ 1 }&\text{ 2 }&\text{ 3 }&\text{ 4 }&\text{ 5 }\\ \hline \text{ FIRST NAME }&\text{ 1 }&\text{ Christa }&\text{ 3 }&\text{ Laura }&\text{ Tom }\\ \hline \text{ SURNAME }&\text{ Gray? }&\text{ Flynn }&\text{ 3 }&\text{ Howe }&\text{ Gray? }\\ \hline \text{ TOPIC }&\text{ BBT }&\text{ P?/Q? }&\text{ SE?/Q? }&\text{ P?/SE?/Q? }&\text{ BH }\\ \hline \text{ LISTENERS }&\text{ 1 }&\text{ few*2 }&\text{ 3 }&\text{ 24 }&\text{ few }\\\hline \end{array}$$

We know that each speech had a different number of participants. It is therefore impossible for Laura to give the pulsar talk if Ed is the 3rd speaker or is Gray.
The second speech can't be about quasars if Ives gives the black hole speech, or point 9 makes the number of people at the black hole speech zero.
A bit of a guess, then, but let's try having Laura give the pulsar talk, with Samuel as the 3rd speaker and Gray giving the black hole talk.
Point 4: Pulsars (assumed Laura, and so 24) = 3rd speaker + Gray
Point 7: 2nd speaker (assumed quasars) = 2* black hole (assumed Gray)
Point 9: Quasars - x = Samuel (assumed 3rd speaker)
This shows us that 3 * Gray - x = 24. The smallest value we can give Gray here whilst making sure we have different numbers of listeners for each talk is 9. This gives us 18 people at the quasar talk, and makes x equal to 3, giving us 15 people at Samuel's talk and 12 at Ives'. Then we just fill in the last couple of gaps, and we can use point 5 to check that this is internally consistent.

$$\begin{array}{|c|c|}\hline\text{ TALK NUMBER }&\text{ 1 }&\text{ 2 }&\text{ 3 }&\text{ 4 }&\text{ 5 }\\ \hline \text{ FIRST NAME }&\text{ Ed }&\text{ Christa }&\text{ Samuel }&\text{ Laura }&\text{ Tom }\\ \hline \text{ SURNAME }&\text{ Ives }&\text{ Flynn }&\text{ Jones }&\text{ Howe }&\text{ Gray }\\ \hline \text{ TOPIC }&\text{ BBT }&\text{ Q }&\text{ SE }&\text{ P }&\text{ BH }\\ \hline \text{ LISTENERS }&\text{ 12 }&\text{ 18 }&\text{ 15 }&\text{ 24 }&\text{ 9 }\\\hline \end{array}$$