Reasoning
Since 210 = 2 x 3 x 5 x 7, 12357 is the only way to get a 5-digit number, in ascending order.
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Puzzle 2
In each of these sentences, can you replace the missing number.
The number is written as a word (e.g. five, twenty-four, thirty-three), and each sentence is correct after the replacement.
This sentence contains ? letters, one hyphen, two commas and a full stop. Interestingly, this sentence contains ? letters, one hyphen, three commas and the final full stop. Finally, this sentence contains ? letters, one hyphen, three commas and one full stop.
Answers This sentence contains sixty-seven letters, one hyphen, two commas and a full stop.Interestingly, this sentence contains eighty-nine letters, one hyphen, three commas and the final full stop.Finally, this sentence contains seventy-nine letters, one hyphen, three commas and one full stop.
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Puzzle 3
At the local mid-summers fayre, four ladies are planning to delight the visitors with their speciality cakes.
Mrs Archer will make a chocolate cake.
Neither Mrs Bowness, Louise nor Kay Cook propose to make a vanilla cake.
Julie, who is not Mrs Dancer, will make coffee.
Mary will not make a plain one.
You need to find their full names and who plans to make which cake.
Answer
Louise Archer will make the chocolate cake.
Julie Bowness will make the coffee cake.
Kay Cook will make the plain cake.
Mary Dancer will make the vanilla cake.
Answer
If the sum of the digits is divisible by nine, so is the number.
Add up all of the digits in the number and see if the sum is divisible by 9. If you still can't tell, you can add those digits again to see if the new sum is divisible by 9. You can keep going until you the sum is obviously divisible by 9 or not.
For example, is 486451464 divisible by 9?
Do 4 + 8 + 6 + 4 + 5 + 1 + 4 + 6 + 4 = 42.
Is 42 divisible by 9? Not sure, you can then do:
4 + 2 = 6. Which clearly isn't divisible by 9. So our original number, 486451464, isn't either.
