Multiple Surprises H.W.
1. If I add the same number to a set of three consecutive numbers, will the new set of numbers be consecutive?
Answer: Yes, If I add the same number to a set of three consecutive numbers, the new set of numbers will be consecutive.
2. If I know that a number is a multiple of 3, what do I need to add to it to get another multiple of 3?
Answer: 3 or a multiple of 3.
3.Which numbers are multiples of 2, 3 and 4?
Answer: Every even number is a multiple of 2. the addition of the digits in a number equals to 3 or a multiple of3 the number is a multiple of 3. every alternate even number is a multiple of 4.
4. Can you use what you have discovered to help you find a few sets of ten consecutive numbers in which:
the
first is a multiple of 1
the
second is a multiple of 2
the
third is a multiple of 3
the
fourth is a multiple of 4
the
fifth is a multiple of 5
the
sixth is a multiple of 6
the
seventh is a multiple of 7
the
eighth is a multiple of 8
the
ninth is a multiple of 9
the
tenth is a multiple of 10?
Answer: Yes, I have used what I learned to find sets of ten numbers which satisfy the given condition.
5. Show several sets you found.
Answer:362881,362882,362883,362884,362885,362886,362887,362888,362889,362890
and 725761,725762,725763,725764,725765,725766,725767,725768,725769,725770.
6.Explain your methods.
Answer: To find a number which is divisible by all numbers from 1 to 10, I multiplied numbers 1 to 9 and arrived at the number 362880. One by one, I added numbers from 1 to10 to 362880 to get a set of 10 consecutive numbers which satisfy the given condition. To get the next set of consecutive numbers, I doubled 362880 and arrived at the number 725760. Then, again one by one, I added numbers from 1 to 10 to get a set of 10 consecutive numbers which satisfy the given condition. So, my conclusion is, you can multiply 362880 by any number and then one by one add numbers from 1 to 10 to get different sets of 10 consecutive numbers which satisfy the given condition.
7.Can you use these ideas to find long sequences of 20
consecutive numbers that do not contain any prime?
Answer: Yes, it is possible to find sets of 20 numbers without any primes.
e.g-51090921717094400002
51090921717094400003
51090921717094400004
51090921717094400005
51090921717094400006
51090921717094400007
51090921717094400008
51090921717094400009
510909217170944000010
510909217170944000011
510909217170944000012
510909217170944000013
510909217170944000014
510909217170944000015
510909217170944000016
510909217170944000017
510909217170944000018
510909217170944000019
510909217170944000020
510909217170944000021