Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,421

Think of two cards

Prepare a deck of twenty cards : the Ace to Ten of Spades and the Ace to Ten of Hearts.
Ask someone to select secretly one Spade and one Heart from the deck, explaining to him/her that an Ace counts as 1.
Now instruct him/her to:
Multiply the value of the Spade by 6.
Add on the value of the Heart.
Double the results.
Subtract the value of the Spade.
Subtract the value of the Heart.

Point out to him/her that, since he/she has now subtracted everything he/she began with, he/she can hardly be giving away any secret by telling you his/her final answer.

Neverhteless, when he/she tells you his/her answer, you proceed to name both the suit and the value of the two cards he/she has chosen.

Can you work out how that detailed information can be derived from the simple answer he/she has given you?

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Think of two cards

If there answer is n, s is the value of the spades, and h is the value of hearts:

s = floor(n/11)
h = n % 11 (where % is the remainder of n / 11)

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,421

Re: Think of two cards

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.