Earlier today I set you the following questions that the authors of Headscratchers, a new puzzle book, suggest are perfect for discussion and solving in licensed premises. The first one, in particular, leads itself to heated debate.
Here they are again with solutions.
1. Creative addition
The numbers 1 to 9 have been written on cards and left on a table.
The left hand column adds to 21; the right to 24. Move a single card so that the two columns add to the same total.
There’s a classic “aha” solution. Yet when this appeared in New Scientist, readers came up with at least ten more solutions. The level of lateral thinking tolerated may depend on personal taste, or on how many pints you have consumed.
Solution
The numbers from 1 to 9 add to 45, which is not divisible by two, so some lateral thinking is required.
The classic solution is to turn 9 upside down to make 6. Then both columns add to 21.
Yet there are many more in this line of thinking. What about placing 1 on top of the 5? Now both columns add to 20. Or you could place the 3 on the 9, or the 5 on the 7.
Please add all your other solutions below the line.
2. The book of numbers
Polly is writing a book containing the whole numbers from zero to infinity in alphabetical order. The first entry is ‘eight’.
What number is second in the list? What number is second-last in the list?
Note: above ‘one quadrillion’ (1015), Polly strings numbers together, ie. 1018 is ‘one thousand quadrillion’
Solution
The second number is ‘eight billion’
The second last number is ‘two trillion two thousand two hundred and two’
(The last number is zero.)
What’s lovely here is that in a list with an infinite number of members it is possible to state the first two, and last two entries.
3. Sick sweeks
Which number is bigger? The product of all the numbers from 1 to 10 (meaning 1 x 2 x 3 x…x 9 x 10, and usually written 10!) or the number of seconds in six weeks?
You are not allowed to solve this one using a calculator!
Solution The numbers are the same.
The number of seconds in six weeks is 6 x 7 x 24 x 60 x 60 = 6 x 7 x (3 x 8) x (5 x 4 x 3) x (5 x 4 x 3) = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
It really is very nice that six weeks of seconds is 10!
It is one of those serendipitous alignments based on our rather arbitrary time measurements. Here are a couple more:
The number of minutes in February is 8!
The number of milliseconds in one day is equal to 55 x 44 x 33 x 22 x 11.
Nice!
I hope you enjoyed today’s puzzles. I’ll be back 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.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
Football School Encyclopedia
I am also the author, together with Ben Lyttleton, of the book series Football School, which explains the world through football. The Football School Encyclopaedia, our first full colour hardback, is out this week! Looking for a gift for a football fan aged 7 or up? It’s an open goal…
