by Danny Roth
Published January 19 2020 (link)
George and Martha and their five daughters with their families have moved into six houses in Super Street. I define a “super prime number” as a prime number which has at least two digits adding up to a prime number (e.g. 11 and 23). Similarly for “super squares” (e.g. 36) and “super cubes”. Houses in Super Street are numbered with the lowest 31 super numbers of the above types.
The elderly couple live in the highest-numbered house on the street. They noticed that the last digits of their daughters’ houses were five consecutive digits and the sum of their five house numbers was a perfect square. Furthermore, the ordinal positions (lowest-numbered house is 1 and so on) of all but one of the houses were prime.
Which five houses did the daughters occupy?
by Howard Williams
Published January 12 2020 (link)
Jenny is pleased that she has found two whole numbers with a remarkable property. One of them is a single digit greater than zero while the other one has two digits. The remarkable thing is that the difference of their squares is a perfect cube and the difference of their cubes is a perfect square.
Her sister Sarah is not impressed, however. She has found two three-digit numbers for which the difference of their squares is also a perfect cube and the difference of their cubes is also a perfect square.
In ascending order, what are the four numbers?
by Andrew Skidmore
Published January 5 2020 (link)
Liam had a bag of snooker balls containing 6 colours (not red) and up to 15 red balls. He drew out balls at random, the first being a red. Without replacing this he drew another ball; it was a colour. He replaced this and drew another ball. This was a red (not replaced), and he was able to follow this by drawing another colour. The probability of achieving a red/colour/red/colour sequence was one in a certain whole number.
After replacing all the balls, Liam was able to “pot” all the balls. This involved “potting” (ie, drawing) red/colour/red/colour…red/colour (always replacing the colours but not the reds), then “potting” the six colours (not replaced) in their correct sequence. Strangely, the probability of doing this was also one in a whole number.
What are the two whole numbers?
by John Owen
Published December 29 2019 (link)
Game show contestants are shown a row of boxes, each containing a different sum of money, increasing in regular amounts (eg, £1100, £1200, £1300, …), but they don’t know the smallest amount or the order. They open one box then take the money, or decline that and open another box (giving them the same choices, apart from opening the last box when they have to take the money).
Alf always opens boxes until he finds, if possible, a sum of money larger than the first amount. Bert’s strategy is similar, except he opens boxes until he finds, if possible, a sum of money larger than both of the first two amounts. Remarkably, they can both expect to win exactly the same amount on average.
How many boxes are there in the game?
by Graham Smithers
Published December 22 2019 (link)
Beth and Sam were using computers to design two table mats shaped as regular polygons.
The interior angles of Beth’s polygon were measured in degrees; Sam’s were measured in grads. [A complete turn is equivalent to 360 degrees or 400 grads.]
On completion they discovered that all of the interior angles in the 2 polygons had the same numerical whole number value.
If I told you the last digit of that number, you should be able to work out the number of edges in (a) Beth’s table mat and (b) Sam’s table mat.
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?