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Jan 13 19

by Brian Gladman

Sunday Times Teaser 2938 – Numerophobia

by Danny Roth

Published January 13 2019 (link)

In Letterland there are no numerals. They use the decimal system of counting just like we do but the digits 0-9 are represented by the first ten letters of the alphabet A-J inclusive but in no particular order. The following calculations are typical:

(1) A + G = C

(2) B x J = FH

(3) GE x AI = HDB

What number is represented by ABCDEFGHIJ?

Jan 6 19

by Brian Gladman

Sunday Times Teaser 2937 – Long Division

by Graham Smithers

Published January 6 2019 (link)

I wrote down a 2-digit number and a 5-digit number and then carried out a long division.

I then erased all of the digits in the calculation, other than the 1’s, and so finished up with the image above.

If I told you how many different digits I had erased, then you should be able to work out my two original numbers.

What were my two original numbers?

Dec 30 18

by Brian Gladman

Sunday Times Teaser 2936 – Multicoloured

by Danny Roth

Published December 30 2018 (link)

George and Martha are selling wall-paper of various colours. By replacing letters with positive digits, they have devised the following multiplication problem:

RED x GREY == YELLOW

The N in GREEN is the remaining positive digit. The red wall-paper is sold only in squares, which is appropriate since RED is a perfect square.

What is the value of GREEN?

Dec 24 18

by Brian Gladman

Sunday Times Teaser 2935 – A Palindrome

by Graham Smithers

Published December 23 2018 (link)

In this Teaser, a jig* is defined as an outwards move to an adjacent empty square, either horizontally, upwards or downwards, the letter * being inserted in all such squares.

Begin with the letter W on a regular grid of empty squares.

From the W, jigO. From every O, jigN. From every N, jigD, and so on until the central diagonal reads SELIM’S TIRED, NO WONDER, IT’S MILES.

Looking at your grid of letters, in how many ways can you trace the palindrome above?

[You can start at any S, move to adjacent letters till you reach the W and then on to any S (including the one you started at). You may move up and down, left and right.]

Dec 16 18

by Brian Gladman

Sunday Times Teaser 2934 – Good Arraz, Baz

by Stephen Hogg

Published December 16 2018 (link)

Baz’s three darts hit the board, scoring different numbers from 1 to 20. “Curious numbers,” said Kaz. Baz looked puzzled. Kaz explained that the first dart’s score to the power of the second dart’s score is a value that contains each numeral 0 to 9 at least once and has the third dart’s score number of digits. Baz only saw that the third dart’s score was the difference between the other two darts’ scores. Kaz wrote the full value on a beer mat. Then Baz put his glass on it and covered most of the value, leaving just the first dart’s score showing to the right and the second dart’s score to the left.

What did each dart score in the order thrown?

Dec 9 18

by Brian Gladman

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?

Dec 2 18

by Brian Gladman

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?

Nov 24 18

by Brian Gladman

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?

Nov 17 18

by Brian Gladman

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?

Nov 10 18

by Brian Gladman

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?