Puzzle 529
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?
Puzzle Copyright © Kevin Stone
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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.
Puzzle 530
You have a barrel, filled to the top with water, which weighs 150 pounds.
What can you add to the barrel in order to make it lighter?
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Hint
Adding just one will be enough.
Puzzle 531
Every year, just before my birthday, I open my money box to see how much money I have saved.
Imagine my surprise when I found exactly £49.58 made up of equal numbers of 2p, 5p, 10p and 20p.
How many of each coin did I find?
Puzzle Copyright © Kevin Stone
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Hint
Remember that you have the same number of each coin.
Answer
134 of each coin.
Reasoning
We have equal numbers of 2p, 5p, 10p, and 20p.
And 2p + 5p + 10p + 20p = 37p.
There are 134 lots of 37p in £49.58.
Double-Checking
134 x 37 = 4958.
Puzzle 532
Assign every letter of the alphabet its numerical value: A=1, B=2, C=3, and so on, up to Z=26.
Can you find any common 6-letter words that have a total over 115?
For example, WIZARD = 23 + 9 + 26 + 1 + 18 + 4 = 81.
Puzzle Copyright © Kevin Stone
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Hint
There are many answers, however, Z doesn't appear very often.
Answer
Choose from: luxury, struts, stylus, syrupy, trusts, twisty.
Other less common words include: scuzzy, syrups, syzygy, trouty, trusty, tryout, trysts.
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