Earlier today I set you these four questions:
1) Volumes I, II and III of a dictionary are stacked vertically side by side on a shelf, in that order and with spines visible in the normal way. The thickness of the pages in each volume is 6cm, and the thickness of the cover of each volume is 5mm.
What is the horizontal distance from the first page of Volume I to the final page of Volume III?
Solution: 8cm
Now this is embarrassing - only 25.06 per cent of you got this one right! More than half – 54.68 per cent – said 20cm. And you may have worked out why you made the mistake as soon as you saw the answer.
When books are stacked in volumes, the first page of each volume ends up on the right side (as you face the shelf) and the last page is on the left side. So to get from the first page of Vol 1 to the last page of Vol 3, you need to count only the thickness of the (front) cover of Vol 1, the (back) cover of Vol 2, the pages of Vol 2, the (front) cover of Vol 2 and the (back) cover of Vol 3. Which is 5mm + 5mm + 6cm + 5mm + 5mm = 8cm
2) Count upwards from ZERO thinking about the letters used in the names of numbers. The letter F appears for the first time in FOUR. The letter A first appears in ONE HUNDRED AND ONE.
Keep on counting, noting the first appearance of each letter in the names of numbers. What is the final letter that you will note down? In other words, when counting upwards, what is the final letter to appear in the name of a number?
Solution: C
By the time we get to 101, we have used 19 letters of the alphabet - leaving B, C, J, K, M, P and Q. Lets tick them off:
MILLION, BILLION, QUADRILLION, SEPTILLION, OCTILLION
So C is the last one to appear. J and K never appear in the name of any number. (Kazillion doesn’t count).
Again, most people got this one wrong. Your favourite choice was Q, with 22.74 per cent, then C (19.72), B (19.44), J (11.95), P (7.65), Y (6.76), M (5.23), K (4.23), and D (2.29).
3) The following statement is correct
< F is the first and the seventh letter of this sentence.>
Using the sentence above as a model, fill in the gap in the following sentence to make it correct:
<C is the first and the [...] letter of this sentence.>
Solution:
C is the first and the forty-sixth letter of this sentence.
4) Reorganise the letters of READING SLOW to form a single word.
Solution:
A SINGLE WORD
Not really a trick question, but required some lateral thought... Congratulations to Andy Knott, who has won a copy of my puzzle book Can You Solve My Problems? for answering the problem correctly.
I hope you enjoyed these puzzles, I’ll be back on September 26.
I post a puzzle here on a Monday every two weeks. If you want to propose a puzzle for this column, please email me I’d love to hear it.
Thanks to Eric Angelini for puzzles 3 and 4 today.
I’m the author of several books on maths, as well as the kids book Football School: Where Football Explains the World which uses football to explain subjects like maths, English, geography, physics, music, fashion, biology and more.
My puzzle book Can You Solve My Problems? is out in November, but you can preorder it here already at a discount.
You can check me out on Twitter, Facebook, Google+, my personal website or my Guardian maths blog.
