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Puzzle 81
My local greengrocer is a would-be mathematician.
She likes to arrange the apples in nice rows.
When she lays the apples in rows of 3, she has one left over.
And, when she lays them in rows of 5, she also has one left over.
Remarkably, she also has one left over when she arranges them in rows of 7 and 9.
But 11 seems to be the magic number, because in rows of 11 there are no apples left over.
Reasoning
We know that (answer − 1) is divisible by 3, 5, 7, and 9.
If it's divisible by 9 then it's automatically divisible by 3.
So the number must be a multiple of 5, 7, and 9.
[5 x 7 x 9 = 315]
Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+ 1).
Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73, and this doesn't work.
Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36, and this doesn't work.
Let's try 3 x 315 + 1: 946 ÷ 11 = 86, and this works, and is the answer.
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Puzzle 82
Below, 10 nine-letter words have been broken into chunks of three letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 10 words are?
ent sen oom ush ile cro
cla rbr ise lis ssr lig
hai mar htn age ess new
sag clo gar ion ing oth
enc ine col our erw cod
Hints
The first letters of the words are: N, C, C, C, E, H, O, C, L, M.
Answers
new + sag + ent = newsagent
cro + cod + ile = crocodile
col + lis + ion = collision
cla + ssr + oom = classroom
enc + our + age = encourage
hai + rbr + ush = hairbrush
oth + erw + ise = otherwise
clo + sen + ess = closeness
lig + htn + ing = lightning
mar + gar + ine = margarine
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Puzzle 83
Can you find the country hidden in the following sentence:
Alex's aches and pains felt worse because of swollen glands that had flared up during the night, perhaps a tonic would help?