Posted in puzzles.

When I was growing up, we had a game called Dingbats - it would offer a sort of graphical cryptic clue to a phrase and you'd have to figure out what the phrase was. For example: West Ham 4-1 Leicester City Chelsea 4-1 Man Utd Liverpool 4-1 Man City Everton

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Posted in arithmetic, puzzles.

An excellent puzzle I heard from @panlepan (I paraphrase, as I've lost the tweet): When you move the final digit of 142857 to the front, you get 714285, which is five times as large. What is the smallest positive integer that is doubled when the last digit moves to the

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Posted in probability, puzzles.

When the redoubtable @cuttheknotmath (Alexander Bogomolny) poses the following question: Two Coins: One Fair, one Biased https://t.co/Rz2zR3LRDj #FigureThat #math #probability pic.twitter.com/HHhnyGjhkq — Alexander Bogomolny (@CutTheKnotMath) March 5, 2018 ... you know there must be Something Up. Surely (the naive reader thinks) the one with two heads out of three is

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Posted in puzzles.

"Your calculator has broken, leaving you with only the buttons for $\sin$, $\cos$, $\tan$ and their inverses, the equals button and the 0 that starts on the screen. Show that you can still produce any positive rational number." When this showed up on Reddit, I knew I was in for

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Posted in puzzles.

One of the puzzles in the MathsJam Shout looked impossible, so obviously I sat down with Mr Miller and had a go at it. I don't have it in front of me, but it went something like: A couple hosts a party to which five other couples are invited. At

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Posted in puzzles.

By way of @ajk_44 at NRICH, a belter of a puzzle: You have 27 small cubes - three each of nine distinct colours. Can you arrange them in a cube so that each colour appears once on each face? (Alison has created a Geogebra widget for you to play with,

Read More →Before I begin: this post involves a puzzle and my attempt at a solution; everything above the horizontal rule is spoiler-free, but go beyond that at your peril. Some days, you can almost hear @colinthemathmo's chuckle as he innocently poses a question such as: Find all configurations of 4 points

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Posted in inequalities, puzzles.

The square root of 2 is 1.41421356237... Multiply this successively by 1, by 2, by 3, and so on, writing down each result without its fractional part: 1 2 4 5 7 8 9 11 12... Beneath this, make a list of the numbers that are missing from the first

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Posted in integration, puzzles.

The brilliant @dragon_dodo sent me this puzzle: Evaluate $\int_0^1 \left(1-x^\frac{1}{7}\right)^3 - \left(1-x^\frac{1}{3}\right)^7 \d x$. I'm not going to give you the solution right now; that will come after I've rambled for a bit. After I'd solved the puzzle (see below), I wondered what each of the integrals actually evaluated to.

Read More →The estimable @colinthemathmo suggests a method for estimating the radius of the earth, which he credits to a sundial expert friend named Mike: Stand on a wall, perhaps two metres high, and wait for sunrise. When you see the sun just peak above the horizon, start the stopwatch, and jump

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