First, as you might know, I have produced a few YouTube videos in my time. Lots of people email me about the music on my videos. Well, they are all produced by the young man in the video below, and now you can employ his services too. So, if you are looking for some great music for a video, feel free to drop him a line.

OK, to the puzzle…..

Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

How can you use 50 American coins to add up to a dollar? The coins available are a penny (1 cent), a nickel (5 cents), a dime (10 cents), a quarter (25 cents), and a half-dollar (50 cents).

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

About a minute. I started at the extreme end, and worked towards the target, but the method I used made me realise there must be loads of combinations that work.

hmmm, i found anwser with FOUR types of coin (though two of them are the same num of coin …. like as if 4×25 and 4×10 (is an example only). not sure if this proofs your presume or not)

Nice puzzle. I found another way of looking at it which made it easy though it did involve a couple of tries, rather than a derived solution. I think there is only one solution.

Also, there are 321 solutions with British coins. 🙂

Silly me. I proved there were no solutions with two quarters and forgot to check solutions with only one! My technique finds that solution – when not used by an idiot 😉 No code, one bit of paper with three lines of five numbers, two of which are the solutions and a bit of mumbling under the breath (“can’t make an odd total out of even numbers so discount that..” etc )

I also proved to my own satisfaction that there are exactly 2 solutions, but sans code. Had a half-hearted go at writing it up as a formal proof, but this was tedious and boring so I stopped. But I could have, if I were motivated.

Two possible answers (one of which only uses three types of coin) – found in a couple of minutes. Then proved with two equations: limiting to positive whole numbers leaves only a handful of scenarios which need to be tested to cover all possible solutions, of which only two work.

1 solution in about 15 seconds. A minute to satisfy myself that there are precisely 2 solutions. There are better coins-to-add-up-to problems than that.

I looked at it and thought – that will be tough. Will be much easier if you can use a 50 cent coin. Then, I saw you could use the 50 cent coin and had it.

My favorite (humorous) puzzle of this type is: 2 coins (American, as in this puzzle) add up to 30 cents. One of them isn’t a nickel. What are they? (answer posted next).

Answer: a quarter and a nickel. (One of them isn’t a nickel–it’s a quarter. The other one is a nickel.)

I dont’ think there’s a solution using a fifty-cent coin.

A solution with a 50 cent coin is impossible. You will be faced with getting 50 cents from the other 49 coins and that’s impossible.

Took me a minute or two to find the four denomination solution.

2 answers in 7 minutes, pen and paper, different approaches and started at the wrong end once I had actually thought about it and applied a bit of common logic

Took me about 5 minutes — using pen & paper.

About a minute. I started at the extreme end, and worked towards the target, but the method I used made me realise there must be loads of combinations that work.

Got an answer in about a minute. Don’t know if there are more. Don’t feel like finding out.

It took me about a minute.

I’m not certain if my solution is the only one.

Took about 10 minutes. Pen and paper and trial and error. (There’s probably an algebraic solution that I’m too dim to work out.)

Took 2 mins and only needed 3 types of coin. I presume there are several other ways…

hmmm, i found anwser with FOUR types of coin (though two of them are the same num of coin …. like as if 4×25 and 4×10 (is an example only). not sure if this proofs your presume or not)

Well that woke me up. About 2 mins

A three denomination answer in reasonably short order.

First time I try the friday puzzle! Only one answer I think (2 equations, 5 unknowns and some limits).

Nice puzzle. I found another way of looking at it which made it easy though it did involve a couple of tries, rather than a derived solution. I think there is only one solution.

I found an answer in a few minutes with trial and error on a scrap of paper.

Another easy excel job.

There are two answers. Took a couple of minutes with a quick bit of code to prove.

Also, there are 321 solutions with British coins. 🙂

Silly me. I proved there were no solutions with two quarters and forgot to check solutions with only one! My technique finds that solution – when not used by an idiot 😉 No code, one bit of paper with three lines of five numbers, two of which are the solutions and a bit of mumbling under the breath (“can’t make an odd total out of even numbers so discount that..” etc )

I also proved to my own satisfaction that there are exactly 2 solutions, but sans code. Had a half-hearted go at writing it up as a formal proof, but this was tedious and boring so I stopped. But I could have, if I were motivated.

Two possible answers (one of which only uses three types of coin) – found in a couple of minutes. Then proved with two equations: limiting to positive whole numbers leaves only a handful of scenarios which need to be tested to cover all possible solutions, of which only two work.

about 2 minutes… used a good old excel sheet to do the math 🙂

1 solution in about 15 seconds. A minute to satisfy myself that there are precisely 2 solutions. There are better coins-to-add-up-to problems than that.

Excel sheet and two minutes.

about 10 minutes

2 mins, threw together a basic spreadsheet and massaged the numbers. Used three of the denominations.

a couple of minutes and python

Easy puzzle.

One answer in about a minute with pencil and paper, working from the smallest upwards. Stopped there.

I have a two answers, each using a different number of coin denominations

Two solutions… and then I found £20 in my pocket!

I looked at it and thought – that will be tough. Will be much easier if you can use a 50 cent coin. Then, I saw you could use the 50 cent coin and had it.

Must be 3 solutions then…

My favorite (humorous) puzzle of this type is: 2 coins (American, as in this puzzle) add up to 30 cents. One of them isn’t a nickel. What are they? (answer posted next).

Answer: a quarter and a nickel. (One of them isn’t a nickel–it’s a quarter. The other one is a nickel.)

I dont’ think there’s a solution using a fifty-cent coin.

A solution with a 50 cent coin is impossible. You will be faced with getting 50 cents from the other 49 coins and that’s impossible.

Took me a minute or two to find the four denomination solution.

Half a minute for one solution with three, another couple of minutes for a solution with four.

Took some time, about 10 mins, through trial and error. Want to know if there’s a more direct way of solving this one.

2 answers in 7 minutes, pen and paper, different approaches and started at the wrong end once I had actually thought about it and applied a bit of common logic

Solved in my head in less than 30 seconds. One coin not used.

There are two unique solutions

Done in 2 minutes, but assuming there are multiple solutions.

Took me about two minutes, which included scrabbling for paper and pencil.

2 answers, couple of minutes

about 10 minutes