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Sunday Afternoon Maths LXVICryptic crossnumber #2
Sunday Afternoon Maths LXVCryptic crossnumber #1
Square and cube endings
Sunday Afternoon Maths LXIVEqual lengths
Sunday Afternoon Maths LXIIIIs it equilateral?
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Square and cube endings
Source: UKMT 2011 Senior Kangaroo
How many positive two-digit numbers are there whose square and cube both end in the same digit?
There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of rectangles (of any size) in a 2×19 grid of squares
There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of squares in a 13×13 grid of squares
What's the star?
In the Christmas tree below, the rectangle, baubles, and the star at the top each contain a number. The square baubles contain square numbers; the triangle baubles contain triangle numbers; and the cube bauble contains a cube number.
The numbers in the rectangles (and the star) are equal to the sum of the numbers below them. For example, if the following numbers are filled in:
then you can deduce the following:
What is the number in the star at the top of this tree?
You can download a printable pdf of this puzzle here.
Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?
Source: Woody at Maths Jam
Multiply together the first 100 factorials:$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.
Lots of ones
Is any of the numbers 11, 111, 1111, 11111, ... a square number?