by Stephen Hogg
Published July 14 2019 (link)
My rest home’s Bingo set uses numbers 1 to 99. To win, nine numbers on your game card must be called. Our caller, not knowing “bingo-lingo”, says “Number 1, total factors 1”, “Number 11, total factors 2” and “Number 30, total factors 8”, etc.
Yesterday, in one game, my hearing aid howled whenever a call started. I missed each number, but heard each “total factors” value. Fortunately, after just nine calls I shouted “HOUSE!” certain that I’d won.
I told my daughter how many different “factor” values I’d heard, but didn’t say what any of the values were. Knowing that I had won after nine calls, she could then be sure about some (fewer than nine) of my winning numbers.
Give, in ascending order, the numbers that she could be sure about?
by Graham Smithers
Published July 7 2019 (link)
For any number, I square the digits and then add the resulting numbers. If necessary, I keep repeating the process until I end up with a single digit, called the result.
For example: 142 gives 1 + 16 + 4 = 21 which then gives 4 + 1 = 5, the result. I have written down a two-digit number.
If I tell you one of the digits [the key digit], you should be able to work out the result.
I then use a 3rd digit to get a three-digit number. The result of that number happens to be the key digit.
In increasing order, what are the three digits?
by Howard Williams
Published June 30 2019 (link)
My wife recently purchased two books from her local bookshop. She showed me the receipt, which showed the cost of each book and the three-figure total cost. I noticed that all of the digits from 1 to 9 had been printed. Coincidentally, exactly the same happened to me when buying two different books, but my more expensive book cost more than hers. In fact, it would not have been possible for that book to have cost more.
How much did I pay for the more expensive book?
by John Owen
Published June 23 2019 (link)
Alan and Cat live in a city which has a regular square grid of narrow roads. Avenues run west/east, with 1st Avenue being the furthest south, while Streets run south/north with 1st Street being the furthest west.
Cat lives at the intersection of 1st Street and 1st Avenue, while Alan lives at an intersection due northeast from Cat. On 1 January 2018, Cat walked to Alan’s house using one of the shortest possible routes (returning home the same way), and has done the same every day since. At first, she walked a different route every day and deliberately never reached an intersection where the Street number is less then the Avenue number. However, one day earlier this year she found that she could not do the same, and repeated a route.
What was the date then?
by Angela Newing
Published June 16 2019 (link)
I recently bought a number of equally priced bags of sweets for a bargain price, spending more than 50p in total. If they had been priced at 9p less per bag, I could have had 2 bags more for the same sum of money. In addition, if each had cost 12p less than I paid, then I could also have had an exact number of bags for the same sum of money.
How much did I spend in total on the sweets?
by Susan Denham
From New Scientist #2161, 21st November 1998
I have just been looking at the top six best-selling books listed in today’s paper. They are numbers from 1 (for the best selling book) to 6, and after each book its position in last week’s list is given.
It turns out that the same six books were in the list last week. For each of the books I multiplied the number of last week’s, and I got six different answers.
Now, if you asked my the following questions — then you would get the same answer in each case:
1. How many primes are there in that list of six products?
2. How many perfect squares are there in that list of six products?
3. How many perfect cubes are there in that list of six products?
4. How many odd numbers are there in that list of six products?
5. How many of the six books are in a higher place this week than last?
For the books 1-6 this week, what (in that order) were their positions last week?
by Eric Emmet
From issue #1647, 14th January 1989
Four football teams are to play each other once. After some of the matches had been played a document giving a few details of the matches played, won, lost and so on was found. This time I am glad to say that, although it was rather a mess, all the figures given were correct. Here it is:
|Team||Played||Won||Lost||Drawn||Goals For||Goals Against||Points|
(Two points are given for a win and one point to each side for a draw.)
Find the score in all the matches that had been played.
by Graham Smithers
Published June 9 2019 (link)
After a day’s filming, a group of those involved in the film’s production went for a gallop.
They split into threes, with a samurai leading each grouping.
The seven samurai were:
BRONSON, BRYNNER, BUCHHOLZ, COBURN, DEXTER, MCQUEEN and VAUGHN
The others involved in the gallop were:
ALANIZ, ALONZO, AVERY, BISSELL, BRAVO, DE HOYOS, HERN,
LUCERO, NAVARRO, RUSKIN, RUSSELL, SUAREZ, VACIO and WALLACH
For each grouping, any two names from the three had exactly 2 letters in common (eg, BRYNNER and BRAVO have B and R in common).
If I told you who accompanied BRONSON, you should be able to tell me who accompanied (a) MCQUEEN and (b) DEXTER
by Danny Roth
Published June 2 2019 (link)
George and Martha are doing a mathematical crossword. There is a 3 x 3 grid with the numbers 1 to 9 inclusive appearing once each. The clues are as follows:
top line: a prime number
middle line: a prime number
bottom line: a prime number
left column: a perfect square
middle column: a perfect square
right column: a prime number
Although you do not need to know this, one of the diagonal three-digit numbers is also prime.
What is the sum of the three “across” numbers?
by Stephen Hogg
Published May 26 2019 (link)
Beyond The Fields We Know
A field named “Dunsany levels” has four unequal straight sides, two of which are parallel. Anne — with her dog, Newton — walked from one corner of the field straight towards her opposite corner. Leon did the same from an adjacent corner along his diagonal. Yards apart, they each rested, halfway along their paths, where Leon, Anne and a signpost in the field were perfectly aligned. Straight fences from each corner converged at the signpost, making four unequal-area enclosures.
Newton made a beeline for the signpost, on which the whole-number area of the field, in acres, was scratched out. Clockwise, the enclosures were named: “Plunkett’s bawn”, “Three-acre meadow”, “Drax sward” and “Elfland lea”. Anne knew that “Three-acre meadow” was literally true and that “Elfland lea” was smaller by less than an acre.
What was the area of “Dunsany levels” in acres?