6
Ok this one's a bit tougher than the "17" problem.
Given an integer that ends with 6 (units column), when you move the 6 from the end to the beginning, the new number is 4 times the original number. What is the smallest number that does the trick?
Pretending that the first number is 3216, we want 4*3216 = 6321.
Obviously this example fails.
Given an integer that ends with 6 (units column), when you move the 6 from the end to the beginning, the new number is 4 times the original number. What is the smallest number that does the trick?
Pretending that the first number is 3216, we want 4*3216 = 6321.
Obviously this example fails.
Labels: mathschallenge
posted by Chris at
10:31 AM
8 Comments:
Hi Chris, you've improved Little Two! The answer is 153846.
Hi quantense. IMO "Little Two" was much better - that had something to get the teeth into. The method I used there, doesn't work for this problem.
You have the correct answer, of course. How did you do it? What's the next number that does it?
My solution is as follows. The number we are seeking ends with 6. Mult. by 4, get 24, so the second digit is 4 and you got 2 in mind. Mult. 4 (the second digit) by 4, got 16, add 2 (was in mind) to 1 (from 16), got 3 and so on, untill you got 6 from 4*1 plus 2, the later is in mind when we come to this step.
To solve it perform multiplication step by step. Each step new digits will come up. When got 6, stop.
Chris, I believe the second is
153846153846.
Hi quantense. You got the next number right too.
Thanks for your explanation. I haven't worked through the problem myself as I pinched it from elsewhere.
I got 153846
which is 1/4 of 615384
Sweet. Multiplying times 5 instead of 4 yields
122448979591836734693877551020408163265306
Watered Almonds, very, very nice. I wish I'd known that result before; I would have posted it instead. Thank you.
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