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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,677

**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?**

Character is who you are when no one is looking.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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)

"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..."

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,677

Character is who you are when no one is looking.

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