1 to 9
The sum of the nine single digits 1,2,3,4,5,6,7,8,9 equals 45
and the product of the nine digits is 362,880.
Find a different string of nine single digits that have the same sum (45) and product (362,880) as the "123456789" string.
(To be different, some digits will be missing and some will occur more than once)
For example, a string of nine digits could be "112233445" but it would not sum to 45, and the product would not be 362,880, so it meets neither condition.
To easily identify a string, put the digits in increasing order.
and the product of the nine digits is 362,880.
Find a different string of nine single digits that have the same sum (45) and product (362,880) as the "123456789" string.
(To be different, some digits will be missing and some will occur more than once)
For example, a string of nine digits could be "112233445" but it would not sum to 45, and the product would not be 362,880, so it meets neither condition.
To easily identify a string, put the digits in increasing order.
Labels: mathschallenge
posted by Ragknot at
3:36 PM
6 Comments:
Another ambiguous question!
Do you mean the sum is to be equal to the product, or do you mean the same sum and product as your example?
If you mean the former, my answer is 1 1 1 1 1 1 1 2 9, but I'm sure that there are many others.
If you mean the latter, that will take a little longer!
Does it have to be from 1 to 9 ?
If single digit numbers are the criteria, 0 0 0 0 0 0 0 0 0 yields a trivial solution
Cam
Oz, unless the problem has been edited, it is not at all ambiguous. It's asking for an array of nine numbers that add up to 45 and multiply to 362880, and is not 123456789.
My solution is 124445799
Also to anonymous, your 000000000 neither adds to 45 nor multiplies to 362880, so I'm a little confused.
Cry Wolf
You have solved it!
Oops, went with vista gadget wording, which is ambiguous. Website wording is clear. Anyway...
To solve for 9 digits from 1 to 9 summing to 45 with product of 362880...
Identify prime factors 1,2,3,5,7
no numbers from 1 to 9 share 5 and 7 as factors, thus 5 and 7 are fixed, solving for 2 numbers
product of 10368 for the remainder or 2^7+3^4=10368. with sum of 33.
Rough checks for value range:
-average value between 4 and 5
-2*7+3*4=29 ...so will need to use higher exponents to bring up sum
-using nine for first 2 digits, 9*2=18, 33-18=15 for remaining 5 digits averaging 3... so use 4s then 2s, then 1s
-Yielding:9,9,4,4,4,2,1
Reordered and incorporating 5 and 7 for final solution...
Answer:
1,2,4,4,4,5,7,9,9
Cam
Cam
Very good reasoning
Good job
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