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Mathematical Puzzles


Difficulty: MediumPuzzle 25

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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Difficulty: EasyPuzzle 26

Puzzle IconWhat number is...

...three quarters of eight ninths of one half of 2001?

[Ref: ZRTD] © Kevin Stone

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Difficulty: EasyPuzzle 27

Puzzle IconMany years ago, a cruise liner sank in the middle of the Atlantic Ocean. The survivors luckily landed on a remote desert island.

There was enough food for the 135 people to last four weeks.

Nine days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 36 people stranded on the island to now share the original rationed food.

The food obviously had to be re-rationed, everyone was now on three-quarters of the original ration, so how many days in total would the food last, from the day of the original sinking?

[Ref: ZJLO] © Kevin Stone

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Difficulty: MediumPuzzle 28

Puzzle IconI recently travelled from my home town to a distant music concert, on a pedal tricycle of all things! My wonderful, three wheeled tricycle.

I knew that the epic 2,345 mile trip would wreak havoc on the tyres, but luckily I took along 4 spares!

Instead of waiting for any single tyre to fail, I decided that I would rotate the tyres evenly, making sure that by the end of the trip all seven tyres had travelled exactly the same distance.

What was the distance that each tyre travelled?

[Ref: ZDFX] © Kevin Stone

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