In my collection of classical music, I have a range of pieces that last 6, 7, 8 and 9 minutes.
The piece by Bach lasts 8 minutes, and the CD lasts longer than the piece by Holst. The piece on DAT tape is longer than the piece by Beethoven. The single lasts 7 minutes, and the album does not contain any Holst. The piece by Butler is on the DAT tape.
Can you determine which piece of music is in which format, and how long each lasts?
Answer Composer Format Length
Beethoven album 6
Holst single 7
Bach CD 8
Butler DAT 9
Reasoning
By (1), the piece by Bach lasts 8 minutes. By (3), the single lasts 7 minutes. Composer Format Length
6
single 7
Bach 8
9
By (4), the piece by Butler is on the DAT tape. But, by (2), this can't be the shortest, so it must be 9 minutes long. Composer Format Length
6
single 7
Bach 8
Butler DAT 9
By (1), the CD can't be the shortest, so must be 8 minutes long. Composer Format Length
6
single 7
Bach CD 8
Butler DAT 9
The album must therefore be 6 minutes long, and by (3) doesn't contain any Holst. Composer Format Length
album 6
Holst single 7
Bach CD 8
Butler DAT 9
Which means that the album was the piece by Beethoven. Composer Format Length
Beethoven album 6
Holst single 7
Bach CD 8
Butler DAT 9
?
Puzzle 131
A parent recently arranged a children's party, and had 187 sweets to give out equally to the children.
Each child had more than one sweet, and there were more children than there were sweets per child.
Answer
There were 17 children, with 11 sweets each.
Reasoning
If we number the clues: each child had more than one sweetthere were more children than there were sweets per child
187 only has the factors 1, 11, 17, 187. Therefore, the only possible answers are:
1 child, with 187 sweets each, which is not allowed by (2)
11 children, with 17 sweets each, which is not allowed by (2)
17 children, with 11 sweets each (*)
187 children, with 1 sweet each, which is not allowed by (1)
Only one possible answer (*) isn't eliminated.
??
Puzzle 132
At my local farmer's merchant, you can buy chicken feed for £4 per tonne, pig feed for £3 per tonne, and cattle feed for 40p per tonne. The feed can only be purchased by the tonne, and part tonnes aren't sold.
Last week I bought some animal feed, and luckily I managed to buy exactly 100 tonnes for exactly £100. How much of each feed did I buy?
Hint
What must the number of tonnes of cattle feed be a multiple of?
Answer
I bought 8 tonnes of chicken feed, 12 tonnes of pig feed, and 80 tonnes of cattle feed.
Reasoning
The number of tonnes of cattle feed must be a multiple of 5, because we need to have a whole number of pounds (5 x 0.40).
If all 100 tonnes was cattle feed, the cost would have been £40, which isn't enough.
If 95 tonnes was cattle feed the cost would have been £38, and the remaining 5 tonnes of (the most expensive) chicken feed at £20, gives a total of £58, which isn't enough.
If 90 tonnes was cattle feed the cost would have been £36, and the remaining 10 tonnes of (the most expensive) chicken feed at £40, gives a total of £76, which isn't enough.
If 85 tonnes was cattle feed the cost would have been £34, and the remaining 15 tonnes of (the most expensive) chicken feed at £60, gives a total of £94, which isn't enough.
If 80 tonnes was cattle feed the cost would have been £32, and the remaining 20 tonnes of (the most expensive) chicken feed at £80, gives a total of £112. So, this might be a possible answer …
We need 20 tonnes of chicken feed and pig feed to equal £68, so let's reduce the chicken feed until it works.
