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Converging Product

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?

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Circles Ad Infinitum

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

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Binary Squares

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

Weekly Challenge 35: Clickety Click and All the Sixes

Stage: 5 Short Challenge Level: Challenge Level:1

This is the live weekly challenge. Our solution to this weekly challenge will appear sometime next Monday, when the next weekly challenge will appear.

We don't publish user solutions for the weekly challenges in the same way as we do for the main problems on the site, but please do discuss the weekly challenges on the Ask NRICH -- follow the link from the main part of the challenge.

Sometimes fascinating extensions and explorations will arise from the challenges. Why not share your thoughts, questions and findings on the Ask NRICH thread?

We hope that you enjoy the challenges.

If you have any comments please email Steve Hewson at post16.nrich@maths.org.




The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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