Logic puzzles


The singers
The students' sum
The coded sum
Other pages in the series
Other pages on this site

What to do

The singers
Here is one I got from Mary Tingblad through the Dead Teachers' Society, and it was Mary who actually inspired me to create this page, when she shared this puzzle with us. Sadly, the rest of this page got shunted to one side until I was redesigning the site in August 2000.

Allen, Bruce, Claire, Donna, and Emma were the top five finishers in their school's talent contest. They finished up filling, in no particular order, 1st, 2nd, 3rd, 4th, and 5th places. Oddly enough, the children came from, in no particular order, 1st, 2nd, 3rd, 4th, and 5th grades! In another startling coincidence, they all performed to the song "My Way" but they all did something different to the music. They either sang, tap-danced, hummed, yodelled, or whistled.

  1. None of the numbers in the order of finish were exactly the same as the grade numbers.
  2. Claire finished in front of Allen but behind the singer, and Donna, and the tap-dancer too, but those last three people are not necessarily in any particular order.
  3. Emma finished behind Bruce but ahead of Donna.
  4. The singer was in 3rd grade and the tap dancer was in 1st grade.
  5. The child that was the hummer deserved to finish in last place and did finish there.
  6. The yodeller was in 4th grade.

Based on the clues, match names with order of finish, grades, and performances. Your task: to try and work out who came where.

This will help you understand

The students' sum
Ivan Sayerspassed this one on to the ABC Science-Matters List -- he tells me it came from a mathematical journal published in Tasmania called DELTA. It may be as old as the hills, but here it is:

Simone and Peter were good maths students, but one afternoon they behaved badly. I told them to come to my classroom at the end of the afternoon. I thought up two numbers between 2 and 200 and when Peter came in I told him the product, (the result of multiplying them). I then told him to sit down and not to mention any number.

I caught Simone outside the door and told her the sum, (the result of adding them). I then told them what I had done and repeated the instruction not to mention a number. (They must not even use the words 'odd' or 'even', because these implicitly refer to the number two !)

I said that each could go home as soon as he/she passed me a piece of paper with the original numbers written on it. A failed trial meant an additional half-hour in class. After a short chat they lapsed into silence.

At about the ten minute mark Peter burst out 'But there's no way I can tell what they are !' Simone grinned 'I could have told you that !', she said. Peter said 'You could?' Simone:'Yup!' Peter thought for a while and passed me a piece of paper. I said he could go.

As Peter sauntered out, Simone's jaw hit the floor. 'He gottem ?', she asked. I nodded. A couple of minutes later Simone grinned again, passed me a piece of paper with the correct numbers written on it, and walked out.

What were the correct numbers ?

By the way, when I put this up on the Web, I was still working on the answer.

This will help you

The coded sum

        D x
        J ÷

This will help you

And now for some help

About the Dead Teachers' Society List
Note -- the Dead Teachers are actually a rather lively bunch! You send a subscribe message reading SUBSCRIBE DTS-L to LISTSERV@LISTSERV.INDIANA.EDU, and away you go. For Science-Matters, the hot link above takes you to a page where you can subscribe.

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Some help

The singers
The main thing with puzzles like this is to set them out well. I drew up a table with headings that said "Place, Grade, Name, Act"
Now straight away, you know that the grade for place 1 can't be 1, and so on. The names I can code as ABCDE, and the acts can be coded as HSTWY. So you write these codes into each of the spaces, and then you start crossing-out.

The main thing to remember is that once you have a cell in the table filled in, you can cross off that choice for all of the other cells in that column. Here is the table after I applied two statements: you work out which ones, and carry on from there.

Place 1 2 3 4 5
Grade 2345 1345 1245 1235 1234

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The coded sum
The main thing with puzzles like this is to start with small things. Look for the multiplication and realise that D can only be 0, 1, 5 or 6, then rule out two of those right away . . . then look at the addition and realise what the value of B is. That's all you get.

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The sums
Ivan's comment to the list: The one 'specialist' fact you need to know is the fact that every even number above four and below a million is the sum of two odd prime numbers. (Number here means positive whole number).

Number freaks will recognize this as a restricted version of the Goldbach conjecture. This is still, so far as I know, unproven, but it has been verified by computer to very high values. (Yes, I have a solution, which I didn't get out of the back of a book.)

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This file is http://www.ozemail.com.au/~macinnis/scifun/logic.htm, first created on October 7, 1998. Last recorded revision (well I get lazy and forget sometimes!) was on April 17, 2005.
Worried about copyright? You need to go look at my fine print. Well, maybe you don't after you read the next paragraph, but do it anyhow . . . and to see some more ideas, look at the start of that same page

©The author of this work is Peter Macinnis -- who is not macinnis@ozemail.com.au**, who asserts his sole right to the product as it is packaged here, recognising that many of the ideas are common. Any non-profit educational or home use is completely acceptable without let or hindrance. Copies of this whole file or site may be made and stored or printed for personal or educational use. The work used here derives from on-going research and development which will one day lead to a book on brain food ideas.
**To make life hard for spammers, that email address does not work. If you add my first name at the front of the address, it WILL work. Think of it as another logic puzzle.
This site had 219,000 hits on the index page from 1999 to January 2007 and an unknown number on other pages. In January 2007, a combined counter was placed on all of the pages, counting page hits which now total