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Posts under Mathemagic

Stacked Deck (part 4)

Posted by DP under Logic, Mathemagic, MathsChallenge, Tom (5 Responds)

Andy, Bob, Charlie, and Dave are ready to play another round of cards. This time it is Charlie’s turn to deal.
The cards are sorted and Charlie decides to only use the Red cards (Hearts & Diamonds).
Three [3] cards are dealt one-at-a-time to each of the four [4] players. Highest pair wins; Aces are low.
If no [...]

The vexatious vault value veracity validation problem

Posted by Chris under Logic, Mathemagic, MathsChallenge (12 Responds)

This problem was originally posted by Karl Sharman (with a less idiotic title).
Whilst I was away under the pretence of work, a nearby bank uncovered a plot to swap the gold in their vaults with counterfeits. It was determined that all the gold bars in three of the Bank’s seven vaults were replaced with counterfeits. [...]

444

Posted by Chris under Mathemagic (9 Responds)

Find all positive integers whose squares end with 444.
Show that no square can end with 4444.

Dicey Dice 2

Posted by DP under Logic, Mathemagic, MathsChallenge, Tom (5 Responds)

There are three fair dice, each numbered 1 through 6; one Blue, one Red, and one Yellow.
You and your opponent will each pick one die and roll. Highest number wins*.
*Special cases:
If there is a tie, and the values are EVEN: Blue beats Red, Red beats Yellow, and Yellow beats Blue.
If there is a tie, and [...]

Dicey dice

Posted by Chris under Mathemagic (8 Responds)

You have three strangely numbered dice A: 3,3,5,5,7,7 B: 2,2,4,4,9,9 and C: 1,1,6,6,8,8
You are invited to gamble using any one of them. The winner is the one who rolls the highest number.
Should you pick your die first, or should you ask the challenger to pick his die first?

777777^333333

Posted by Chris under Mathemagic (4 Responds)

What is the last digit of 777777333333?
Although I’ve only used 7’s and 3’s, you should be able to generalise the 777777 and 333333 to get the same result.

Weigh hay

Posted by Chris under Logic, Mathemagic (9 Responds)

A farmer asked a worker to weigh 5 trusses of hay. The fool weighed them two at a time in all possible ways, and found that the weights were:
110, 112, 113, 114, 115, 116, 117, 118, 120, and 121 units.
What are the weights of the individual trusses?

Yellow streak

Posted by Chris under Logic, Mathemagic (6 Responds)

As the last one was easy, here’s another already.
A banana seller sells half his bananas plus half a banana on the first day. He does the same the next day, and the next day, and so on, until he finally runs out of bananas at the end of the tenth day. How many bananas did [...]

Barrel of beer

Posted by Chris under Logic, Mathemagic (8 Responds)

A man bought 6 barrels of booze. 5 contained wine and one contained beer. The sizes of the barrels were 15, 16, 18, 19, 20 and 31 gallons (luvvly jubbly). He sold a number of barrels of wine to one customer, and later sold some more barrels of wine to another customer. The second customer [...]

Round Robbin’

Posted by Chris under Logic, Mathemagic (8 Responds)

Seven gents A,B,C,D,E,F and G play a silly game. In order of their names, each doubles the amount of money that the others have in their pockets (from his own pocket). i.e. the money simply gets redistributed.
When all seven have taken their turn, each ends up with $128.
How much money did each of the gents [...]

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