## Friday, 29 May 2015

### Solving logic problems

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 hummed, sang, tap-danced, whistled or yodelled.

Based on the clues, match names with order of finish, grades, and performances.

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.
First, we need to work out what the variables are that we have to slot in, We have the names, ABCDE, we have the grades, 12345, and the places 12345, and the performances, hstwy. Now we are ready to begin.
The trick is to draw up a table, and then begin eliminating the impossibles. To give you a start, I have applied two statements: you can carry on from there.

After applying statement 1:
 Place 1 2 3 4 5 Grade 2345 1345 1245 1235 1234 Name ABCDE ABCDE ABCDE ABCDE ABCDE Performance hstwy hstwy hstwy hstwy hstwy

After applying statement 2:
 Place 1 2 3 4 5 Grade 2345 1345 1245 1235 1234 Name BDE BDE BDE C A Performance hstwy hstwy hstwy hwy hwy

After applying statement 3:
 Place 1 2 3 4 5 Grade 2345 1345 1245 1235 1234 Name B E D C A Performance hstwy hstwy hstwy hwy hwy

Now go back an apply statement 2 again...

From here, you're on your own :-)

General note that I am adding to some of my blog entries: I have lots of different interests. If some area interests you, look at the very end and you will see a set of tags called labels. These are hot links that will give you a list of other articles with the same tag/label.