Puzzle : Draw The Maximum Sum

Assume you are blindfolded and placed in front of a large bowl containing currency in $50, $20, $10, and $5 denominations. You are allowed to reach in and remove bills, one bill at a time. The drawing stops as soon as you have selected four-of-a-kind— four bills of the same denomination. 

What is the maximum sum of money you could accumulate before the drawing ends?

THIS should be the maximum sum! 

Source

The Maximum That You Can Get!

What was the question?

The quick response to the question by any body would be 3 x 50 + 1 x 20 = $170 would be the maximum as next pick of highest currency of $50 will stop drawing of currencies. But that 5th attempt may not be of $50 & could be of $20,$10 or $5. So this case doesn't count those possibilities. This is worst case scenario where 3 out of 4 picks resulted into accumulation of 3 currencies of same denomination of $50.

So ideally, after drawing three $50 s, three $20 s, three $10 s, three $5 s and finally drawing one anything will stop drawing attempts as that will accumulate 4 bills of same denomination (of $50/$20/$10/$5). The best that can be picked is $50 to get the maximum.

That is total maximum of 50 x 3 + 20 x 3 + 10 x 3 + 5 x 3 + 50 = $305 can be accumulated in 12 attempts & stopping after 13th attempt. And this will be the best case.

Spot The Liar Among

There is a party of 100 politicians. All of them are either honest or liars. You walk in knowing two things:

1. At least one of them is honest.

2. If you take any two politicians, at least one of them is a liar.

From this information, can you know how many are liars and how many are honest?

Know the total number of liars here! 

Source

Knowing The Number of Liars

What is the question?

The information that we have - 

1. At least one of them is honest.

2. If you take any two politicians, at least one of them is a liar. 

Only one of them must be honest and other 99 must be liars. 

Those are the only numbers that can justify the second piece of information. In the case, if any 2 are selected at least 1 of them liar while other may or may not liar (i.e. may be honest).