by Stephen Hogg
Published December 15 2019 (link)
The Prhymes’ triple live album “Deified” has hidden numerical “tricks” in the cover notes. Track 1, with the shortest duration, is a one-and-a-half minute introduction of the band, shown as “1. Zak, Bob, Kaz 1:30” in the cover notes. The other nineteen tracks each have different durations under ten minutes and are listed similarly with durations in “m:ss” format.
For each of tracks 2 to 20, thinking of its “m:ss” duration as a three-figure whole number (ignoring the colon), the track number and duration value each have the same number of factors. Curiously, the most possible are palindromic; and the most possible are even.
What is the total album duration (given as m:ss)?
by Angela Newing
Published December 8 2019 (link)
My telephone has the usual keypad:
1 2 3
4 5 6
7 8 9
My telephone number starts with 01 and ends in 0. All digits from 2 to 9 are used exactly once in between, and each pair of adjacent digits in the phone number appear in a different row and column of the keypad array.
The 4th and 5th digits are consecutive as are the 9th and 10th and the 8th digit is higher than the 9th.
What is my number?
by Victor Bryant
Published December 1 2019 (link)
In the classroom I have a box containing ten cards each with a different digit on it. I asked a child to choose three cards and to pin them up to make a multiplication sum of a one-figure number times a two-figure number. Then I asked the class to do the calculation.
During the exercise the cards fell on the floor and a child pinned them up again, but in a different order. Luckily the new multiplication sum gave the same answer as the first and I was able to display the answer using three of the remaining cards from my box.
What was the displayed answer?
by Danny Roth
Published November 24 2019 (link)
George and Martha have their five daughters round the dinner table. After the meal, they had ten cards numbered 0 to 9 inclusive and randomly handed two to each daughter. Each was invited to form a two-digit number. The daughter drawing 0 obviously had no choice and had to announce a multiple of ten.
However, the others each had the choice of two options. For example if 3 and 7 were present, either 37 or 73 would be permissible. George added up the five two-digit numbers (exactly one being divisible by 9) and Martha noticed that three of the individual numbers divided exactly into that total.
What was the total of the remaining two numbers?
by Graham Smithers
Published November 17 2019 (link)
My local antiques dealer marks each item with a coded price tag in which different digits represent different letters. This enables him to tell the whole number of pounds he paid for the item. I bought a tea pot from him tagged MOE.
Inside the tea pot was a scrap of paper which I used to work out his code. The letters AMOUNT I SPENT had been rearranged to make the multiplication sum above.
How much did he pay for the tea pot?
by Howard Williams
Published November 10 2019 (link)
Judith is a keen walker who uses a five-digit pedometer to record her number of steps. Her pedometer is inaccurate as some of the counters consistently move on to 0 early by missing out one or more digits. For instance, one of them might roll over from 7 to 0 every time instead of from 7 to 8, missing out digits 8 and 9. She is, however, well aware of this and can work out the correct number of steps.
After walking her usual distance, the pedometer shows 37225 steps but she knows that the true number is 32% less than this. A second distance she walks requires a 30% reduction in the number displayed to give the true number of steps.
How many steps is the second distance?
by Susan Bricket and John Owen
Published November 3 2019 (link)
We were wondering why ancient Egyptians chose to represent arbitrary fractions as sums of distinct unit fractions of the form 1/n (thus 5/7 = 1/2+1/5+1/70). One of us recalled long ago watching our greengrocer use four brass weights of 1/2, 1/4, 1/8, 1/16 lb to weigh any number of ounces up to 15 by stacking some of them on one side of her balancing scales. We wanted to make a metric equivalent, a set of distinct weights of unit fractions of a kilo, each weighing a whole number of grams, to weigh in 10g steps up to 990g.
Naturally, we wanted to use as little brass as possible, but we found that there were several possible such sets. Of these, we chose the set containing the fewest weights.
List, in increasing order, the weights in our set.
by Richard England
From New Scientist #2142, 11th July 1998
A semi-prime is the product of two prime numbers; the square of a prime counts as a semi-prime.
Harry, Tom and I were trying to find pairs of 2-digit semi-primes such that if we added the two semi-primes together we formed a 2-digit prime. We each found three such pairs; the 18 semi-primes we used and the 9 primes that were formed were all different.
Harry’s three odd semi-primes were all greater than 50; Tom’s three even semi-primes were all greater than 50.
What were my three pairs of semi-primes?
by Graham Smithers
Published October 27 2019 (link)
I set Sam a question, the answer to which was a 3-digit number, with the digits increasing by 1 from first to last (eg 789)
Sam eventually produced a 3-digit answer, but only 2 of his digits were correct and in the correct position. The third digit was wrong.
Investigating further I found that Sam had the correct answer but, for devilment, decided to change it into a different (single-digit) base.
If I were to tell you which of his 3 digits was the wrong one, you should be able to tell me:
(a) the correct answer, and
(b) the base used by Sam.
by Andrew Skidmore
Published October 20 2019 (link)
Sam has purchased Norfolk Flats; an area of farmland (less than 100 hectares) bordered by six straight fences. He intends to farm an area which is an equilateral triangle with corners that are the midpoints of three of the existing boundaries. This creates three more distinct areas (one for each of his sons); these areas are identical in shape and size and have two sides that are parallel.
Sam measured the area (in square metres) which each son will farm and also his own area. One of the numbers is a square and the other a cube. If I told you which was which, you should be able to work out the area of Norfolk Flats.
What (in sq metres) is that area?