# Sunday Times Teaser 2933 – Sunday Teaser

### by Graham Smithers

#### Published December 9 2018 (link)

I wrote down two three-figure numbers and worked out their product by long multiplication. Systematically replacing digits by letters, my workings became:

 ________________ N T S E D S — — — D U R S Y R D A N D U — — — — — — A R R A T S — — — — — —

I then wrote down two numbers which were represented by SUNDAY TEASER.

What were these two numbers?

# Sunday Times Teaser 2932 – Triangulation

### by Andrew Skidmore

#### Published December 2 2018 (link)

Liam plans to make a set of dominoes. They will be triangular, and one face of each domino will have a number at each corner. The numbers run from 0 up to a maximum digit (9 or less), and the set is to include all possible distinguishable dominoes.

With the maximum digit he has chosen the set would contain a triangular number of dominoes. [A triangular number is one where that number of balls can fit snugly in an equilateral triangle, for example the 15 red balls on a snooker table]

How many dominoes will he need to make?

# Sunday Times Teaser 2931 – Unfortunate 57

### by Susan Bricket

#### Published November 25 2018 (link)

In the early days of the internet, I used a secret shorthand for my important passwords: Bank=1/7, Credit Card=2/7, ISP=3/7, etc. Like all fractions, the decimal expansions

$\frac{1}{7} = 0.142857142857142 …, \frac{2}{7} = 0.285714285714285 …$

eventually repeat themselves, in this case in sequences of six digits. In each case, my password was the set of digits that repeat (“Unfortunate 57” is a mnemonic for 142857). As password requirements became stricter, I changed my system to base 11, using an X for the extra digit for “ten”; so for instance in base 11

$234 =1×11^2 + 10×11^1 + 3 ×11^0 = 1X3_{11}$

and

$\frac{1}{2} =0.5555 … = \frac{5}{11^1} +\frac{5}{11^2} + \frac{5}{11^3} + …$

In the sequence 1/2, 1/3,…, what is the first password of length greater than six that my base-11 system produces?

# Sunday Times Teaser 2930 – Odd Socks

### by Victor Bryant

#### Published November 18 2018 (link)

I had a drawer containing some black socks and some white socks. If I drew out two socks at random the chance of getting a black pair was 1 in …

After many washes all the socks looked grey. So I added some red socks to the drawer. Then if I drew out two at random the chance of getting a grey pair was 1 in …

After many washes all the socks looked pink. So I added some green socks to the drawer. Then if I drew out two the chance of getting a pink pair was 1 in …

After many washes all the socks looked brown. So I have now added some yellow socks to the drawer giving me a total of fewer than fifty socks. Now if I draw out two the chance of getting a brown pair is 1 in …

The gaps above consist of four different prime numbers.

If I draw out two socks at random, what is the chance of getting a yellow pair?

# Sunday Times Teaser 2929 – My Pin Numbers

### by Graham Smithers

#### Published November 11 2018 (link)

Using all but one of the digits 0 to 9, and systematically replacing them by a letter, my pin numbers become ONE, TWO, FIVE and SEVEN.

These numbers are such that:

ONE is odd

TWO is even

FIVE is odd and divisible by 5

SEVEN is divisible by 7

ONE + TWO + TWO = FIVE

If I told you which digit was not used, you should be able to work out my pin numbers.

What pin number is represented by SEVEN?

# Sunday Times Teaser 2928 – Golf Balls

### by John Owen

#### Published November 4 2018 (link)

Three friends play 18 holes of golf together every week. They have a large supply of golf balls numbered from 1 to 5. At the beginning of a year, they each start playing with a new ball, but all three ball numbers are different. Alf uses the same ball number for exactly 21 holes before changing to the next higher number (or to number 1 if he was using a number 5). He continues to use each number for exactly 21 holes. The same applies to Bert, except that he changes his ball number in the same way after every 22 holes, and to Charlie who changes his ball number after every 23 holes.

Last year, there was just one occasion when they all used the same ball number on a hole.

What was the number of the hole on that occasion?

# Sunday Times Teaser 2927 – On a Roll

### by Stephen Hogg

#### Published October 28 2018 (link)

My son saw the “average sheets per roll” printed on our new pack of four toilet rolls. Curious, he counted each roll’s total sheets by overlaying lines of ten sheets to and fro, tallying layers, and then adding any extra sheets. These totals were four consecutive three-figure numbers, including the printed “average sheets per roll”. For each total, he noticed that there was the same single-figure number of choices for a number of sheets per layer, requiring at least two layers, which would leave no extra sheets. Re-counting the toilet roll with the “average sheets per roll”, he used a two-figure number of sheets per layer and tallied a two-figure number of such layers, with no extras.

What was the “average sheets per roll”?

# Sunday Times Teaser 2926 – Coins of Obscura

### by Peter Good

#### Published October 21 2018 (link)

George and Martha were on holiday in Obscura where coins are circular with radii equal to their whole number value in scurats. They had coffees and George took out some loose change. He placed one 10 scurat and two 15 scurat coins on the table so that each coin touched the other two and a smaller coin between them that touched all three. He then placed a fifth coin on top of these four which exactly covered them and the total value of the five coins was exactly enough to pay the bill.

How much was the coffee bill?

# Sunday Times Teaser 2925 – “The Eternal Triangle” — Go Figure!

### by Stephen Hogg

#### Published October 14 2018 (link)

From my desk I saw the above when Leigh and Bob put 8392546137 and 4613725808 into two of the identical calculators used by my class. Everyone was told to press “clear”, then enter their unique three-figure pupil number (between 100 and 999) and divide this by the total number of display segments seen in it. If the result was a whole number they were to repeat the process with that result and its segment count (and so on until a decimal fraction part arose). Leigh, Bob and Geb each made four “divisions” this way. Using their three initial values as the sides of a triangle (Bob’s shortest, Geb’s longest), I told them to find its area.

What was Leigh’s number?

# Sunday Times Teaser 2924 – Snaking Up

### by Victor Bryant

#### Published October 7 2018 (link)

A “Snakes and Ladders” board consists of a 10-by-10 grid of squares. In the first row (at the bottom) the squares are numbered from 1 to 10 from left to right, in the second row the squares are numbered 11 to 20 from right to left, in the third they are 21 to 30 from left to right again, and so on.

An ant started on square 1, moved to square 2 and then, always moving to an adjacent square to the right or up, it finished in the top-right corner of the board. I have added up the total of the numbers on the squares it used and, appropriately, the total is a perfect square. In fact it is the square of one of the numbers the ant visited — the ant passed straight through it without turning.

What was that total of the numbers used?