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.
The results of a recent Chess tournament between five close rivals is described below:
Dale finished before Alex. Emery finished after Bailey. Alex finished before Chris. Emery finished after Dale. Bailey finished before Alex. Dale finished after Bailey. Chris finished before Emery.
Who finished where?
Hint
Try rewriting each statement so that they are all 'finished before' statements instead.
Answer
Bailey won …
… then Dale, Alex, Chris, and Emery.
Reasoning
By placing the person who finished higher to the left, we have:
Dale finished before Alex (Dale > Alex)Emery finished after Bailey (Bailey > Emery)Alex finished before Chris (Alex > Chris)Emery finished after Dale (Dale > Emery)Bailey finished before Alex (Bailey > Alex)Dale finished after Bailey (Bailey > Dale)Chris finished before Emery (Chris > Emery)
From (1) and (3):
Dale > Alex > Chris
Adding (7):
Dale > Alex > Chris > Emery
Adding (6):
Bailey > Dale > Alex > Chris > Emery
Which is the final placing for all the players, and can be double-checked with the remaining clues.
The first group of trainee astronauts are all sitting around the table, waiting to start their first day of training.
From the clues given below, can work out where everyone sits?
Seat 1 is next to Seat 2 and Seat 8, etc. Seat 5 is across from Seat 1, and Seat 7 is across from Seat 3, etc. Seat 2 is a higher seat number than Seat 1, etc.
William is next to Alisa and Nick. William is across from George. Amanda is next to Sarah. Sarah is across from Eric. Nick is next to Eric. Sydney is in Seat 4 and sits next to George. George has a higher seat number than Sydney. Alisa is not in Seat 2.
Answer
Seat 1 = William
Seat 2 = Nick
Seat 3 = Eric
Seat 4 = Sydney
Seat 5 = George
Seat 6 = Amanda
Seat 7 = Sarah
Seat 8 = Alisa
Reasoning
Sydney is in Seat 4 and is next to George (Clue 6), so George is in either Seat 3 or Seat 5. But George has a higher seat number than Sydney (Clue 7). Therefore, George is in Seat 5.
William is across from George (Clue 2), and therefore is in Seat 1.
William is next to Alisa and Nick (Clue 1), so Alisa and Nick are in Seat 2 and Seat 8 (either way around). But Alisa is not in Seat 2 (Clue 8). Therefore, Alisa is in Seat 8 and Nick is in Seat 2.
Nick is next to Eric (Clue 5) so can only be in Seat 3.
Sarah is across from Eric (Clue 4), and therefore is in Seat 7.
Amanda is next to Sarah (Clue 3) and can only be in Seat 6.
