Posted in geometry, Uncategorized

If you’ve read this blog for a while, you’ll know I’m a fan of @cshearer41’s puzzles (her book, Geometry Puzzles in Felt Tip, is available wherever etc). At a recent MathsJam, one jumped out of Chalkdust at us: (Image from Issue 10 of Chalkdust, a magazine for the mathematically curious.)

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Posted in ask uncle colin

Dear Uncle Colin, How many zeros are there on the end of $100!$? I worked it out to be 21, but the answer sheet says it’s 23 – and my calculator just gives an error message. What do you think? - Maybe A Tutor Has Exact, Reasoned Response? Hi, MATHERR,

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Posted in algebra

Suppose we have $ax^2 + bx + c = 0$. It’d be easier to complete the square if the $x$ term were even, so let’s double: $2ax^2 + 2bx + 2c = 0$ It’s also be nicer if the $x^2$ term were a square, so let’s multiply by $2a$: $4a^2x^2

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Posted in ask uncle colin

Dear Uncle Colin, I have an exam question I don’t understand! There’s a toy truck of mass 5kg attached (by a rod) to another truck of mass 2kg on a slope at 10 degrees to the horizontal. The resistances to motion are 8N and 6N, respectively, and the whole thing

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Posted in dome

One of the questions that occasionally crops up in the hive of scum and villainy I hang out in search of problems to solve is, “how do calculators work out trigonometric values?”. It’s not, typically, the way that the Mathematical Ninja would (find an angle nearby and adjust using heuristics),

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Posted in ask uncle colin

Dear Uncle Colin, I need to figure out $\int \cos^3(2t) \sin^5(2t) \dt$ and I’m… just going round in circles. So to speak. What do you suggest? - Doing Integration’s Really A Chore Hi, DIRAC, and thanks for your message! It’s very easy to end up going around in circles on

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Posted in puzzles

A nice puzzle by way of @benjaminleis: This AIME problem is fun: pic.twitter.com/DhbviTqnqr — Benjamin Leis (@benjamin_leis) February 2, 2020 In case you can’t read that, we need to find the sum of the digits in $N = 9 + 99 + 999 + 999\dots999$, where the last number consists

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Posted in ask uncle colin

Dear Uncle Colin, I want to stretch my Year 12 Further Maths class - what extra-curricular topics would you recommend? Something To Really Engage Their Creative Reasoning Hello, STRETCH, and thanks for your message! How excellent to be looking beyond the curriculum for ways to engage and develop your young

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Posted in number theory

I’m in the process of clearing out old bookmarks, and stumbled on this puzzle from @jase_jwanner: Prime or not prime? No calculators allowed!a. 23567897614^2 - 1b. 34564344^3 -1c. 76543556556625731d. 345643554^{10} - 169 — Jase (@jase_jwanner) August 27, 2016 I shall give you a moment to ponder these, and put my

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Posted in ask uncle colin

Dear Uncle Colin, I’ve figured out that $x^{x^{x^{\dots}}} = 2$ when $x = \sqrt{2}$, but I’m struggling to make sense of the function - it seems to have a vertical gradient when $x = e^{\frac{1}{e}}$, but it doesn’t seem to have what I think of as an asymptote there. What

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