Can you solve it? Ace of spades

<span>Photograph: Estate Of Keith Morris/Getty Images</span>
Photograph: Estate Of Keith Morris/Getty Images

In the immortal words of Lemmy from Motörhead: “I don’t share your greed, the only card I need is the ace of spades.”

Whether or not this was in response to the following puzzle is for you to decide.

1. Deck dilemma

Your friend choses at random a card from a standard deck of 52 cards, and keeps this card concealed. You have to guess which of the 52 cards it is.

Before your guess, you can ask your friend one of the following three questions:

  • is the card red?

  • is the card a face card? (Jack, Queen or King)

  • is the card the ace of spades?

Your friend will answer truthfully. What question would you ask that gives you the best chance of guessing the correct card?

2. Heart is in pieces

The image below is a spade. Can you cut it into three pieces such that it is possible to reassemble the pieces and make a heart?

To be clear, what you are being asked to do is this: imagine the spade is made of card. Make two cuts to the card, thus cutting it into three pieces, and then reassemble the pieces without overlapping so that the pieces together make the shape of a heart, that is, the symbol of the suit of hearts. The cuts may, or may not, be straight lines.

I’ll be back at 5pm UK today with the solutions. PLEASE NO SPOILERS. Instead reminisce about Lemmy.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

The first puzzle is adapted from Basic Probability, What Every Math Student Should Know by the eminent Dutch mathematician Henk Tijms. If you are interested in probability, and want an accessible, historical take, you might enjoy the following book by Henk’s son Steven Tijms: Chance, Logic and Intuition: An Introduction to the Counter-Intuitive Logic of Chance.

The origin of the second puzzle is either Sam Loyd or Henry Dudeney, who both published the puzzle around 100 years ago.

I’m the author of several books of puzzles, most recently the Language Lover’s Puzzle Book. I also give school talks about maths and puzzles (restrictions allowing). If your school is interested please get in touch.