What a series!

Number Theory Level 3

Complete the number series.

(This doesn't have a mathematical function, it has a logical rule)

288, 468, 486, 648, 666, 684, _ _?

844 886 846 822 864 828 866 800

Archit Boobna by Archit Boobna , 20, India

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2 solutions

Archit Boobna
Mar 17, 2015

This is a series of numbers with even digits and are multiples of 9.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

nice qusetion

tanveen dhingra - 6 years, 2 months ago

The digits of those numbers also sum up to make 18.

Manmeswar Patnaik - 6 years, 2 months ago

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Yes, that is a good observation. It is a direct consequence of the rule and of the fact that the numbers are 3 digit numbers.

Archit Boobna - 6 years, 2 months ago

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Check the dispute

tanveen dhingra - 6 years, 2 months ago

Why not 864 and 846.

Ankit Kumar Jain - 6 years, 2 months ago

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Please check my comment in the disputes category. I am sure that you will be able to get your answer there.

Manmeswar Patnaik - 6 years, 2 months ago

There is another logical pattern that dictates 864 as the correct answer. In particular, if we think of each digits as being a bucket from left to right holding a given number of balls (so in the first instance, there are 2 balls in the first bucket, 8 balls in each of the second and third buckets), then we take 2 balls from from the first bucket having 8 balls and put them in the one before (so we see 288-->468-->486-->...). The number with 666 will have all entries checked up until the last one, in which case we find none have 8 balls, hence we take from the last bucket we've checked. This then means the last number ought to be 864.

CJ Lungstrum - 6 years ago
Ken Ken
May 14, 2015
  • 288: 2+8+8 = 18
  • 468: 4+6+8 = 18
  • 486: 4+8+6 = 18
  • 648: 6+4+8 = 18
  • 666: 6+6+6 = 18
  • 684: 6+8+4 = 18
  • 828: 8+2+8 = 18

sum: 4068: 4+0+6+8 = 18

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