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Puzzle 73
At my local farmer's merchant, you can buy chicken feed for 15c per tonne, pig feed for $1.25 per tonne, and cattle feed for 40c 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 are the maximum and minimum tonnes of pig feed I could have bought?
Answer
I bought 15 tonnes of chicken feed, 75 tonnes of pig feed, and 10 tonnes of cattle feed.
15 x 0.15 = 2.25 75 x 1.25 = 93.75 10 x 0.40 = 4.00
100 tonnes = $100.00
A possible solution method follows …
I couldn't have bought 80 tonnes of pig feed because this would have cost the full $100.00, but I wouldn't have then had 100 tonnes in total.
Similarly, 70 tonnes of pig feed would have been too few, as this would cost $87.50 and even the remaining 30 tonnes all being cattle feed wouldn't have reached the required $100.00.
So, let's try 71 tonnes of pig feed = $88.75:
plus 1 x chicken feed + 28 x cattle feed is over $100.00 or 2 x chicken feed + 27 x cattle feed is under $100.00
so 71 tonnes of pig feed doesn't work.
Let's try 72 tonnes … and so on.
We soon get to 75 tonnes of pig feed and find the answer.
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Puzzle 74
Below you can find a proverb.
The letters have been converted to their location in the alphabet.
Four clowns were getting ready for the evening's performance. From the clothes trunk, each clown had to get their socks and shoes.
There was one pair of shoes in each colour, and one pair of socks in each colour.
Can you tell who had which colour socks and which colour shoes?
The red socks went with the blue shoes. Baba had yellow shoes, but not yellow socks. The clown with green shoes did not have blue socks. Boba had neither red shoes nor red socks. Bilpo's shoes were the same colour as Babil's socks. The clown with red shoes had green socks.
Hint
Try matching the sock colours to the shoe colours first.
Answer
Baba
Blue socks and Yellow shoes.
Boba
Yellow socks and Green shoes.
Bilpo
Green socks and Red shoes.
Babil
Red socks and Blue shoes.
Reasoning
We had these colours: Red, Blue, Yellow, Green.
We had these clowns: Baba, Boba, Bilpo, Babil.
Let's match sock colours to shoe colours.
By (1) Red socks went with Blue shoes.
By (6) Green socks went with Red shoes.
By (3) Yellows socks must have gone with Green shoes.
Therefore, Blue socks went with Yellow shoes – confirmed with (2).
In summary: Socks : Shoes
Red : Blue
Green : Red
Yellow : Green
Blue : Yellow
By (2) Baba had Blue socks and Yellow shoes.
By (4) Boba didn't have Red socks or Red shoes (and Baba had the Blue socks), so must have had Yellow socks and Green shoes.
By (5) Bilpo's shoes were the same colour as Babil's socks – we only have Red & Green socks left, and Blue & Red shoes. Therefore, Babil's socks can only have been Red (with Blue shoes).
Leaving Bilpo with Green socks and Red shoes.
Double-Checking
1. The red socks went with the blue shoes [Babil].
2. Baba had yellow shoes but not yellow socks [had Blue].
3. The clown with green shoes did not have blue socks [had Yellow].
4. Boba had neither red shoes nor red socks [had Green shoes and Yellow socks].
5. Bilpo's shoes were the same colour as Babil's socks [Red].
6. The clown with red shoes had green socks [Bilpo].
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It is now three years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
