Can yule solve it? We need to talk about 2024

For the first time in eight years of posting puzzles on alternate Mondays, today’s publication date coincides with Christmas Day. Festive greetings everyone!

What numerical gifts has Santa brought this year? For North Americans, there’s a delightful date next week: New Year’s Eve is 123123.

Now let’s turn our thoughts to 24, the number of the coming year.

Puzzle 1 Can you make 24 using only the digits from 1 to 9 and the basic arithmetical operations? Here’s one way that places all the digits in the correct order.

(1²³⁴⁵⁶ x 7) + 8 + 9

Beginner level: find another way.

Advanced level: find another way with the digits in reverse order.

[By basic arithmetical operations I mean +, –, x, ÷, exponent, brackets, and concatenation, i.e. when you run numbers together as in ‘23456’ above. If you get stuck, as a gesture of festive goodwill, I will also allow square roots and decimal points.]

Smashed it

Talking of numbers, I would like to thank the readers of this column for making this year its most successful ever. In 2023 the column has received more than 5.3 million page views – a 36 per cent increase on 2022. Way to go, puzzlers!

The most popular column of this year by far was The simple question almost everyone gets wrong, which featured a task invented a century ago for testing children’s IQs . (The backstory of the puzzle is as heartwarming as any a Christmas tale.)

Since I figured you liked this problem, I asked Jane Braybrook, who rediscovered the puzzle when looking for ways to help her disabled son with his cognitive development, to produce some new examples. Here they are:

Puzzle 2 In each of the examples below, the shapes A to L are either blocks of colour or stencils (i.e. squares with holes in.) The shape on the top is made by placing some of A to L on top of each other. Your task is to work out which stencils/blocks are used and in which order.

PLEASE NO SPOILERS. Instead please discuss your favourite facts about the number 24.

I’ll be back at 5pm UK with solutions.

UPDATE: The solutions are available here.

Thanks to Inder Taneja, who every Christmas compiles a whole document of amazing number facts about the coming year, including the example above. His website is a cornucopia of numerical curiosities.

Thanks to Jane Braybrook for the stencil puzzles. You can find more of them on her app Stenciletto, which can be downloaded from www.smileyworldgames.com.

Finally, I am still pinching myself that I was asked to represent my alma mater, Corpus Christi College, Oxford, on this year’s Christmas University Challenge. It was a dream come true. Fingers on buzzers! Starter for ten! Last week we won our first round bout against Edinburgh University. We appear in the semi-final on Wednesday, 8.30pm on BBC2. Wish us luck!

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

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