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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?
Ted thinks of a three-digit number. He removes one of its digits to make a two-digit number.
Ted notices that his three-digit number is exactly 37 times his two-digit number. What was Ted's three-digit number?
If A, B, C, D and E are all unique digits, what values would work with the following equation?$$ABCCDE\times 4 = EDCCBA$$
Six different (strictly) positive integers are written on the faces of a cube. The sum of the numbers on any two adjacent faces is a multiple of 6.
What is the smallest possible sum of the six numbers?
Today's number is the smallest number with exactly 28 factors (including 1 and the number itself as factors).
In the song The Twelve Days of Christmas, how many presents have been given after 8 days?
The factors of 6 (excluding 6 itself) are 1, 2 and 3. \(1+2+3=6\), so 6 is a perfect number.
Today's number is the only three digit perfect number.