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Medium Puzzles


Difficulty: MediumPuzzle 17

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: MediumPuzzle 18

Puzzle Icon

Greenjack Round #1

You find yourself playing a game with your friend.

It is played with a deck of only 16 cards, divided into 4 suits:

   Red, Blue, Orange and Green.

There are four cards in each suit:

   Ace, King, Queen and Jack.

Ace outranks King, which outranks Queen, which outranks Jack - except for the Green Jack, which outranks every other card.

If two cards have the same face value, then Red outranks Blue, which outranks Orange, which outranks Green, again except for the Green Jack, which outranks everything.

Here's how the game is played: you are dealt one card face up, and your friend is dealt one card face down. Your friend then makes some true statements, and you have to work out who has the higher card, you or your friend. It's that simple!

Round 1:
You are dealt the Green Ace and your friend makes three statements:

1. My card is higher than any Queen.
2. Knowing this, if my card is more likely to beat yours, then my card is Blue. Otherwise it isn't.
3. Given all of the information you now know, if your card is more likely to beat mine, then my card is a King. Otherwise it isn't.

Who has the higher card, you or your friend?

[Ref: ZGQN] © E.J. Shamblen

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Difficulty: MediumPuzzle 19

Puzzle IconIf four kittens can catch four mice in four minutes...

...how many mice can twelve kittens catch in twelve minutes?

[Ref: ZLCG] © Kevin Stone

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Difficulty: MediumPuzzle 20

Puzzle IconUsing all of the letters A to Z, each once only, complete these common words:

ban*
*a*i*et
*aiz*
s**th
na*e*
*eco*
*ocu*
*la*e
**nk
f*x
be**re
e*ui*
ot*er
wis*
*oast

[Ref: ZVZH] © Kevin Stone

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