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### Which number is the odd one out?

January27

These talented young dancers are doing a routine for a judge – who will score them using their numbers. Above them are two more numbers, making the sequence 5, 7, 2, 5 or (top to bottom) 7, 5, 5, 2. My students enjoyed coming into class and, when seeing four numbers on the board, trying to find the odd one out. Many times, there is more than one answer. For example, with the numbers 1,2,3,4 two are even and two are odd and two are prime. So, which one is the odd one out? You might suggest that it is number 4, since it is the largest – or 1 because it is the smallest. Both answers are correct.

Now, back to the picture (taken yesterday) – 7, 5, 5, 2. Which one is odd? They are all prime numbers, so that doesn’t help, although I could notice that the sum of 7+5+5+2 is also a prime number.

I might choose the number 2 as the odd one out, simply because there is a bigger gap between the 2 and the other numbers. But, of course, you might find another one that is odd – perhaps one of the 5’s? Why? Because 5+2=7, leaving a lonely number 5 as the odd one out!

“No, no,” you might say, “It is the number 7, because 5×5=25 which ‘uses up’ the number 2, leaving the 7 as the odd one out!”

“But,” another might protest, “7-5=2, leaving the number 5 on its own!”

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#### Post Support

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]