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Puzzle of the day

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Mark P
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PostPosted: Fri May 11, 2018 2:10 am 
Post subject: Re: Puzzle of the day

kbrazell wrote:
Mark P wrote:
Damocles wrote:
What sort of weighing are we talking?

Do you have a balance thing or digital scales?

If it's digital, 9. If it's a balance jobby 5.


Digital.

The answer is once.


This is the analog scale version

I've not done the math but I think the answer has something to do with mixing the stacks while keeping track the stack from which each coin originated.

Something along the lines of swap 1 coin from stack 1 and stack 6, 2 from stack 2 and 7.
Where stacks 1-5 are measured on one side and 6-10 on the other.

The digital may be the same. Take 1 coin from stack 1, 2 from stack 2. So you know some number of fakes are in your measure. You'll have all ten coins from stack 10. Your total new stack will have 10+9+8+7+6+5+4+3+2+1 = 55 coins. Since you know what that ought to weigh, the number of grams different from that tells you which stack was bogus.


Correct.

Next one and something a bit different:

New Year’s Day normally falls one week after Christmas; if Christmas falls on a Thursday, then New Year’s Day will fall on a Thursday as well. What is the most recent year in which Christmas and New Year’s Day fell on different days of the week?

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Lee Drake
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PostPosted: Tue May 15, 2018 9:52 am 
Post subject: Re: Puzzle of the day

I had to Google it, so I will not give it away. The answer is simple once you realize a detail.
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Mark P
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PostPosted: Mon May 21, 2018 5:27 am 
Post subject: Re: Puzzle of the day

Lee Drake wrote:
I had to Google it, so I will not give it away. The answer is simple once you realize a detail.


Indeed; a good one that needs no mathematical ability.


Here's one that requires slightly more than zero mathematical ability, but not much.

How many unique pairs of prime numbers can be added together to make 999?

HINT: Analysis should take far longer than testing.

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Marek Chladny
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PostPosted: Mon May 21, 2018 5:53 am 
Post subject: Re: Puzzle of the day

I would say that only one such par exists: 2, 997

Except the number 2, all other prime numbers are odd. Adding 2 odd numbers gives an even number. However, we need to get the odd number 999. Therefore no other pairs of prime numbers other than (2,997) are a solution.

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Mark P
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PostPosted: Wed May 23, 2018 3:26 am 
Post subject: Re: Puzzle of the day

Marek Chladny wrote:
I would say that only one such par exists: 2, 997

Except the number 2, all other prime numbers are odd. Adding 2 odd numbers gives an even number. However, we need to get the odd number 999. Therefore no other pairs of prime numbers other than (2,997) are a solution.


Correct - no mathematical ability needed beyond recognizing that odd + odd = even and that the only prime even number is 2.

And now this:

How quickly can you find out what is unusual about this paragraph? It looks so ordinary that you would think that nothing was wrong with it at all and, in fact, nothing is. But it is unusual. Why? If you study it and think about it you may find out, but I am not going to assist you in any way. You must do it without googling for solutions. No doubt, if you work at it for long, it will dawn on you. Who knows? Go to work and try your skill. Par is about half an hour.

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