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Dec 1 23

Sunday Times Teaser 3193 – Balanced Education

by BRG

by Danny Roth

Published Friday December 01 2023 (link)

George and Martha are headmaster and secretary of Millimix School. There are 1000 pupils divided into 37 classes of at least 27 pupils each; each class has at least 13 members of each sex. Thus with 27 x 37 = 999, one class has an extra pupil. The classes are numbered 1-37.

Martha noted that, taking the class with the extra pupil, and adding its class number to the number of girls in that class and a power of two, she would arrive at the square of the class number. Furthermore, the class number equalled the number of classes in which the girls outnumbered the boys.

How many boys are in the school?

Nov 24 23

Sunday Times Teaser 3192 – In Formation Technology

by BRG

Football formations are generally described by three or four nonzero whole numbers summing to 10 (the goalkeeper isn’t counted), representing, from defence to attack, the number of players in approximate lines across the pitch.

Last season we played a different formation every week, always using four lines, each with at most four players; the difference between one week and the next was that from one line two players moved, one to an adjacent line and the other to the line beyond that (eg, 3-4-1-2 could only be followed by 3-2-2-3). Our number of fixtures was the largest it could have been, given these conditions. The first number in our formations was more often 3 than any other number; 3-1-3-3 gave us our worst result.

How many games did we play, and what were our first three formations?

Nov 17 23

Sunday Times Teaser 3191 – The Budgie’s Extra Ration

by BRG

by Paul Hughes

Published Friday November 17 2023 (link)

The budgie’s circular toy hung on a hook. Two equal legs suspended his budgerigar-seed dispensing chord from that hook. Parallel to the chord, a diameter crossed the middle. When budgie knocked his seed dispenser below the diameter, a triangle lit up, as shown, and he got an extra seed ration. In the design of the toy, the ratio of the length of the chord to the length of the smallest side of the lit triangle has been adjusted so that a right-angled triangle results, with the right angle on the diameter.

What is the square of that ratio?

Nov 10 23

Sunday Times Teaser 3190 – Mods-In-Suits

by BRG

by Stephen Hogg

Sunday November 12 2023 (link)

In single-pack card game Mods-In-Suits, players are dealt two cards. Each card’s face value (Ace=1 to K=13) is modified by its suit, thus: “Spade” squares it; “Heart” halves it; “Club” changes its sign; “Diamond” divides it by the other card’s face value. Players score their modified values’ sum (or zero if there is a matching pair of face values). Players may exchange their second dealt card for a fresh card from the pack.

Stuck in the jam in the Smoke at rush hour, John’s children were missing Andy’s party. Playing Mods-In-Suits for amusement led to one unusual game. Jo’s initial score was a positive whole number, Bo’s its negative. Four different suits and face values were dealt. Both exchanged their second card, but each score was unchanged. Four different suits were still showing.

Give Jo’s final hand.

Nov 3 23

Sunday Times Teaser 3189 – Telling Tiles

by BRG

by Victor Bryant

Published Sunday November 05 2023

I have four tiles with a digit written on each of them: I shall refer to these as A, B, C and D. I have rearranged the tiles in various ways to make two 2-figure numbers and I have then multiplied those two numbers together (eg, CB times AD). In this way I have found as many answers as possible with this particular set of tiles and I have discovered that

I. The number of different answers is AB.

II. Of those answers B consist of the four digits A, B, C, D in some order.

III. There are C other 4-figure answers.

What are A, B, C and D respectively?

Oct 27 23

Sunday Times Teaser 3188 – Royal Mail Slims Down

by BRG

by Susan Bricket

Published Sunday October 29 2023 (link)

The Royal Mail, facing stiff competition, was looking for ways to streamline and simplify its operations. One dotty idea circulating in 2022 was to sell only two face values of postage stamps. Customers would then need to be able to make up 68p for a second-class letter and all values above 68p, to be ready for subsequent price rises. An obvious solution would be to sell only 1p and 68p stamps. But this would mean sticking 28 stamps on a first-class letter (costing 95p), leaving little room for the address!

Which two stamp values would minimise the total number of stamps required to post two letters, one at 68p and one at 95p, and still allow any value above 68p to be made up?

Oct 20 23

Sunday Times Teaser 3187 – Wired Squares

by BRG

by Mark Valentine

Published Sunday October 22 2023

Sitting at his study desk one morning, Ted noticed a paperclip poking out of his notebook, unbent to a straight thin wire. Opening it up he found that his granddaughter Jessica had drawn a square grid (less than 14cm [1] side width) on one of the pages, with vertical and horizontal grid lines at 1cm intervals.

Musing this, Ted numbered each cell consecutively from 1, working left to right along each row from top to bottom in turn. Moving the wire over the page, he rested the wire over (or touching the corner of) some cells containing a square number. Placing the wire carefully, he was able to connect as many square-numbered cells as possible in this way. No square grid of less than 14cm [1] side width could have allowed the connection of a larger number of squares.

What squares did he connect?

[1] This was originally 15cm when first published.

Oct 13 23

Sunday Times Teaser 3186 – Contemporary Classmates

by BRG

by Edmund Marshall

Published Sunday October 15 2023 (link)

In our local school, the year begins on September 1 and ends on August 31, and class one contains all the children who reach the age of five during the school year. I was looking back at the school records and discovered that one year during the 1980s, it so happened that the birthdays of a group of children in class one fell on the same-numbered day of different months and also on the same day of the week. The size of this group was the largest possible for these circumstances, and by coincidence the number of classmates in the group was also the number of the day in the month for their birthday. The oldest member of that group, whose birthday was in January, was born in the 1980s.

What was the full date of birth of the youngest member of that group?

Oct 10 23

Sunday Times Brainteaser 1702 – And Now Not One Is …

by BRG

By Victor Bryant

Published 30th April 1995

In what follows, digits have been replaced by letters, a different letter being used consistently for each different digit. There are no zeros.

Each of the recurring decimals:


equals a fraction with a denominator less than 50. And now not one is easy to find.

Please find what is DONE.

Oct 6 23

Sunday Times Teasers 3185 – Multiple Squares

by BRG

by Howard Williams

Published Sunday October 08 2023 (link)

My grandson likes to compile 3×3 magic squares, where each of the three rows of numbers, each of the three columns of numbers and both of the straight diagonals, add up to the same total. This he did without repeating any of the nine numbers in the square.

He has now progressed to compiling similar 3×3 squares, which instead of the eight rows, columns and diagonals of numbers adding to the same total, they instead multiply to produce the same product. In his first such square this product was 32,768. He was able to find every square of nine different whole numbers that gives this product, excluding identical rotational and mirrored squares.

What, in ascending order were the totals of the nine numbers in each of his different squares?