Maths Investigation

Card Trick Puzzler

A magic maths workshop is a great way to enthuse your children and get them excited about maths.

The following trick is perfect for a maths investigation for your school maths week or as a maths problem solving activity. The trick is easy to demonstrate and is self working. All you require is a pack of ordinary playing cards.

Maths Workshop

Maths Workshop

Here is what you do:

  1. Have a volunteer shuffle the cards using any method they prefer.
  2. Explain that you want them to turn the deck of cards over and look at the value of the bottom card. Place this card face down on the table and then turn the pack over so that it is also face down and deal off cards from the top of the pack  up to the value of twelve and place them one at a time on top of the original card face down card forming a pile. For example, if the value of the first card on the bottom of the deck was six it would be placed face down on the table. The pack is turned over and cards are dealt from the top of the pack, the next card counting as seven, then eight, nine etc up to twelve. ( All picture cards are given a value of ten ).
  3. Demonstrate the above to be sure that your volunteer understands your instructions.
  4. Have them reshuffle the cards then turn away leaving them to make a pile of cards as described.
  5. Now ask them to continue repeating the process until all of the cards are used up.
  6. When they come to the last pile, if the last cards will not count to twelve they are put to one side as a remainder.
  7. When they have finished you turn round and announce that you will state exactly the total obtained by adding up the value of the bottom card of every pile even though you are unable to see any of the cards because all of the plies of cards are face down.
  8. You then glance down at the piles of cards and after a few moments thought declare a number.
  9. The volunteer turns over all of the piles of cards and adds up the value of each one. The grand total is the same as the number you declared.
  10. You bow modestly.

How to work out the answer:

When you turn round count how many piles of cards there are and subtract four. Whatever you are left with multiply by thirteen and then add to this the number of cards left over. This will be the total.

Example:

There are nine piles of cards.

9 – 4 = 5

5 x 13 = 65

Lets say there were three left over cards.

65 + 3 = 68

The sum of the values of the bottom card on every pile will be 68.

 

Problem solving

For a school problem solving activity or as a maths investigation have your pupils work in pairs or small groups. Give each group a pack of fifty two playing cards and ask them to try out trick for themselves. Once they are confident in the execution of the trick ask them to explain why it works.

Book a Magic Maths Workshop for your school.

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