Fight with Eight

By

KT Rajagopalan

The question:

Prof Math E W is at it again. He tells the class: ‘You can make 6! = 6*5*4*3*2*1 = 720 six-digit numbers using each of the digits between 1 and 6 inclusively exactly one time each.’

He asks them for a few examples.

Anil calls out ‘123456 itself!’ Priya says, ‘346125’ while Siddharth says, ‘112345’ and all others cry out, ‘No, it is not such a number: 1 is repeated and 6 is not used at all!’

‘Okay, my question is: How many of these 6-digit numbers are divisible by 8?’

Anil, Shreya, Priya and Siddharth come up with the answers: 120, 72, 90 and 84 respectively.

Who is right, if at all? (a) Anil (b) Shreya (c) Priya (d) Siddharth (e) None 

Would you like a hint?

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