Puzzle 257
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?
Puzzle Copyright © Kevin Stone
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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.
20 chicken + 0 pig = 80 + 0 = £80
19 chicken + 1 pig = 76 + 3 = £79
18 chicken + 2 pig = 72 + 6 = £78...
We can see it's coming down 1 at a time, so we need to come down to a total of £68, which is 10 fewer tonnes of chicken feed:
8 chicken + 12 pig = 32 + 36 = £68. As required.
Double-Checking
8 x 4.00 = £32.00
12 x 3.00 = £36.00
80 x 0.40 = £32.00
--- ------
100 tonnes = £100.00
Puzzle 258
Starting with SOFT, change one letter at a time until you have the word LENS.
Each change leaves the other letters in their original places and must result in a proper word.
What is the minimum number of steps required to achieve this change?
SOFT
....
....
....
LENS
Puzzle Copyright © Kevin Stone
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Hint
The first change makes SOFT into LOFT.
Answer
SOFT, LOFT, LEFT, LENT, LENS.
Puzzle 259
What are the next 3 digits in this sequence:
7 3 1 8 2 8 5 3 1 5 3 0 3 3 1 4 3 0 {?} {?} {?}
Puzzle Copyright © Kevin Stone
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Hint
This question involves the months of the year in some way.
Answer
4 3 1.
Reasoning
This is the sequence of the length of the name of the month and the number of days in that month.
For example, January has 7 letters and 31 days: 7 3 1.
February has 8 letters and 28 days, etc.
The next 3 digits are therefore 431 since July has 4 letters and 31 days.
Puzzle 260
What is the next number in this sequence:
1 1 2 4 3 9 4 61 5 52 6 63 7 94 8 {?}
Puzzle Copyright © Kevin Stone
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Hint
Can you see 1, 2, 3...?
Answer
46.
Reasoning
Take the numbers in pairs, square the first, and reverse the digits.
1 1 (1 x 1 = 1, reversed is 1)
2 4 (2 x 2 = 4, reversed is 4)
3 9 (3 x 3 = 9, reversed is 9)
4 61 (4 x 4 = 16, reversed is 61)
5 52 (5 x 5 = 25, reversed is 52)
6 63 (6 x 6 = 36, reversed is 63)
7 94 (7 x 7 = 49, reversed is 94)
so we require:
8 46 (8 x 8 = 64, reversed is 46)
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