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Mathematical Puzzles


Difficulty: MediumPuzzle 1

Puzzle IconA large fresh water reservoir has two types of drainage system: small pipes and large pipes.

6 large pipes, on their own, can drain the reservoir in 12 hours.

3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.

How long will 5 small pipes, on their own, take to drain the reservoir?

[Ref: ZHRT] © Kevin Stone

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Difficulty: EasyPuzzle 2

Puzzle IconLast weekend I was given my pocket money, which is meant to last me all week.

On Monday, I spent a quarter of my money on clothes.

On Tuesday, I spent one third of my remaining money on a CD.

On Wednesday I spent half of my remaining money on sweets.

Finally on Thursday I spent my last £1.25 on a comic.

How much pocket money did I receive?

[Ref: ZZJG] © Kevin Stone

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Difficulty: EasyPuzzle 3

Puzzle IconThree teachers were discussing how long they had been teaching.

Adrian and Betty had been teaching for a total of 36 years.

Charles and Betty had been teaching for a total of 22 years.

Charles and Adrian had been teaching for a total of 28 years.

How long had each been teaching?

[Ref: ZKLD] © Kevin Stone

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Difficulty: MediumPuzzle 4

Puzzle IconTommy: "How old are you, Mamma?"

Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."

Tommy: "That's a lot, isn't it? And how old are you, Papa?"

Papa: "Just six times as old as you, my son."

Tommy: "Shall I ever be half as old as you, Papa?"

Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."

Tommy: "And supposing I was born before you, Papa; and supposing Mamma had forgot all about it, and hadn't been at home when I came; and supposing..."

Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."

Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of Mamma?

[Ref: ZPYU] Mamma's Age. Amusements In Mathematics by Henry Ernest Dudeney (1917).

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