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MEI Conference - Sessions about famous mathematicians
The 2015 MEI conference featured a strand of sessions about 12 famous mathematicians. The following problem is from the session about John Conway.
There are only three numbers (>1) that can be written as the sum of fourth powers of their digits:
1634 = 14 + 64 +34 +44
8208 = 84 + 24 + 04 + 84
9474 = 94 + 44 + 74 + 44
Find the smallest number (>1) that can be written as the sum of fifth powers of its digits.
This year the 2016 Conference will feature a strand of sessions about a different set of 12 famous mathematicians. To see details of these, and other sessions, visit the conference website: conference.mei.org.uk
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What’s the area?
Now read the research: Drawing attention to a lack of attention
A cube is sliced vertically along the line shown in the diagram and the smaller part is thrown away.
The remaining prism is going to be sliced vertically downwards again by a line going through corner D.
Where would the slice have to be to split it into two equal volumes?
This problem is taken from the FMSP GCSE Problem Solving Materials.
50, 60, 70, ... ?
Find the size of the angle α.
2016 is a triangular number.
The first three triangular numbers are: 1, 3, 6. The first three pentagonal numbers are: 1, 5, 12.
The pentagonal numbers 1, 5 and 12 are all one third of a triangular number.
Are all pentagonal numbers one third of a triangular number?