Earlier today, I presented you with a series of questions from Headscratchers, a recently published puzzle book. The authors recommend discussing and solving these questions in licensed establishments. The first question, in particular, is likely to spark intense discussion.

Here are the solutions for them once more.

1. Creative addition

Nine cards with the numbers 1 to 9 have been placed on a table.

The sum of the numbers in the left column is 21, while the sum of the numbers in the right column is 24. Rearrange one card to make both columns have the same total.

There is a well-known solution that evokes an “aha” moment. However, after being featured in New Scientist, readers proposed at least ten additional solutions. The degree of creativity allowed may vary depending on individual preferences or the amount of alcohol consumed.

Solution

The sum of the numbers 1 to 9 is 45, which cannot be divided by two. Therefore, a different approach is needed.

One traditional method is to rotate the number 9 to create a 6, resulting in both columns equalling 21.

However, there are numerous other possibilities to consider. For example, what if we placed 1 above the 5? This would result in both columns adding up to 20. Alternatively, we could place the 3 on top of the 9, or the 5 on top of the 7.

Please include any additional solutions below the designated line.

2. The book of numbers

Polly is creating a book that lists whole numbers from zero to infinity in alphabetical order. The initial entry is ‘eight’.

Which number is listed second? Which number is listed second-to-last?

^15) is not ‘one quadrillion’

Note: Numbers above 10^15 are not considered to be equivalent to one quadrillion. ^{15}), Polly strings numbers together, ie. 10^{18} is ‘one thousand quadrillion’

Solution

The number following is ‘8,000,000,000.’

The number before the last one is ‘two trillion two thousand two hundred and two’.

(The final number is zero.)

One great aspect is that in a list with an unlimited amount of items, it is feasible to identify the first two and last two elements.

3. Sick sweeks

Which number is greater? The result of multiplying all the numbers from 1 to 10 (also expressed as 1 x 2 x 3 x…x 9 x 10 and commonly written as 10!) or the total number of seconds in six weeks?

Using a calculator is not permitted for solving this problem.

The values are identical.

There are 604,800 seconds in six weeks.

It really is very nice that six weeks of seconds is 10!

This is a fortunate coincidence that relies on our subjective units of time. Here are a few additional examples:

The number of minutes in February is 8!

,400,000

There are 5,400,000 milliseconds in a day.^{5} x 4^{4} x 3^{3} x 2^{2} x 1^{1}.

Nice!

I hope you had a good time solving today’s puzzles. I will return in two weeks.

Today’s puzzles all come from Headscratchers: The Puzzle Book by Rob Eastaway and Brian Hobbs. Rob curates the New Scientist’s weekly puzzle and the puzzles in the book are taken from its pages. It’s a fantastic and varied collection of problems authored by some of the best puzzle setters around.

Every other Monday, I post a puzzle on this platform. I am constantly searching for interesting puzzles. If you have any suggestions, please send me an email.

I co-authored the book series Football School with Ben Lyttleton. This series uses football to help explain various topics. Our first full color hardback, the Football School Encyclopaedia, is now available! If you’re searching for a gift for a football fan who is 7 years or older, this is a perfect choice.

Source: theguardian.com