The Miller next took the company aside and showed them nine sacks of flour that were standing as depicted in the sketch.
"Now, hearken, all and some," said he, "while that I do set ye the riddle of the nine sacks of flour.
And mark ye, my lords, that there be single sacks on the outside, pairs next unto them, and three together in the middle thereof.
By Saint Benedict, it doth so happen that if we do but multiply the pair, 28, by the single one, 7, the answer is 196, which is of a truth the number shown by the sacks in the middle.
Yet it be not true that the other pair, 34, when so multiplied by its neighbour, 5, will also make 196.
Wherefore I do beg you, gentle sirs, so to place anew the nine sacks with as little trouble as possible that each pair when thus multiplied by its single neighbour shall make the number in the middle."
As the Miller has stipulated in effect that as few bags as possible shall be moved, there is only one answer to this puzzle, which everybody should be able to solve.
The Miller's Puzzle, The Canterbury Puzzles, Henry Ernest Dudeney.
Hint
The two left numbers multiplied, or the right two numbers, should create the central number.
Answer
The way to arrange the sacks of flour is as follows: 2, 78, 156, 39, 4. Here each pair when multiplied by its single neighbour makes the number in the middle, and only five of the sacks need to be moved.
There are just three other ways in which they might have been arranged (4, 39, 156, 78, 2; or 3, 58, 174, 29, 6; or 6, 29, 174, 58, 3), but they all require the moving of seven sacks.
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Puzzle 202
Hidden in these sentences are the numbers 1 to 10 (in words).
A number might appear in more than one sentence, and they might not be in order, but there is only one way to use all of the sentences and find all ten numbers.
The robins love hiding amongst the smooth reeds. It's always worth looking after your friends, even if they've upset you. Even heavyweight boxers like using soft tissues when they have a cold. To avoid the cliff, I veered sharply to the left. The eggs were boxed thirteen instead of a dozen in each baker's delivery box. Having salmon every day for lunch gets a little boring after a while. The attendance at the local football match exceeded last week's by many thousands. We need to waterproof our boots to make sure we don't get wet. Meeting friends after work allows executives to network effectively. The orchestra sounded magnificent with the three virtuosi xylophonists.
Answer Having salmON Every day for lunch gets a little boring after a while.Meeting friends after work allows executives to neTWOrk effectively.The robins love hiding amongst the smooTH REEds.We need to waterprooF OUR boots to make sure we don't get wet.To avoid the clifF, I VEered sharply to the left.The orchestra sounded magnificent with the three virtuoSI Xylophonists.It's always worth looking after your friendS, EVEN if they've upset you.Even heavywEIGHT boxers like using soft tissues when they have a cold.The eggs were boxed thirteen instead of a dozeN IN Each baker's delivery box.The atTENdance at the local football match exceeded last week's by many thousands.
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Puzzle 203
Yesterday I was asked to buy some stamps.
In the land of BrainBashers, stamps are available in denominations of 3p, 9p, 11p, 17p, and 21p (just the five different values).
For three denominations of stamp I was asked to buy eight of each, and for the other two denominations I was asked to buy nine of each.
Unfortunately, I forgot which I was supposed to buy eight of, and which to buy nine of!!
Luckily I had been given the exact money required to buy the stamps, £5.00, so the shopkeeper was able to work out the stamps I needed.
Answer
Eight lots of 11p, 17p and 21p, and nine lots of 3p and 9p.
Reasoning
For three denominations of stamp I was asked to buy 8 of each, and for the other two denominations I had to buy 9 of each.
So I had to buy at least 8 of all five denominations.
This would be for a total of 8 x (3 + 9 + 11 + 17 + 21) = 488p = £4.88.
The remaining 12p has to buy the remaining 2 stamps, which must have been 3p and 9p.
Double-Checking
9 x 3 = 27
9 x 9 = 81
8 x 11 = 88
8 x 17 = 136
8 x 21 = 168
For a total of 27 + 81 + 88 + 136 + 168 = 500p = £5.
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Puzzle 204
Farmer Stone is quite an eccentric dairy farmer.
He originally had a total of 54 gallons of milk in three churns, and he wanted to make sure each churn contained 18 gallons of milk.
In order to do this, he did the following:
First, he poured 1/4 of the first churn into the second churn. He then poured 1/2 of the second churn into the third churn. Finally, he poured 1/3 of the third churn into the first churn.
How many gallons did each churn contain before Farmer Stone started pouring?
Hint
Try working backwards, with each churn containing 18 gallons.
Answer
12, 33, and 9 gallons respectively for churns 1, 2, and 3.
Reasoning
Working backwards, at the end after Pour 3, the churns (C1, C2, C3) contained:
C1 C2 C3
————————————
18 18 18 after Pour 3
Pour3 was 1/3 of C3 into C1, the remaining 2/3 has to be the 18 gallons left in C3 after the pour, which means that 1/3 is 9 gallons. So 9 gallons was poured from C3 into C1. Before Pour3, C1 must have contained 9 gallons, and C3 contained 27 gallons.
C1 C2 C3
————————————
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour2 was 1/2 of C2 into C3, the remaining 1/2 has to be the 18 gallons left in C2 after the pour, which means that 1/2 is 18 gallons. So 18 gallons was poured from C2 into C3. Before Pour2, C2 must have contained 36 gallons, and C3 contained 9 gallons.
C1 C2 C3
————————————
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
Pour1 was 1/4 of C1 into C2, the remaining 3/4 has to be the 9 gallons left in C1 after the pour, which means that 1/4 is 3 gallons. So 3 gallons was poured from C1 into C2. Before Pour2, C1 must have contained 12 gallons, and C2 contained 33 gallons.
C1 C2 C3
————————————
12 33 9 at the start
9 36 9 after Pour 1
9 18 27 after Pour 2
18 18 18 after Pour 3
