perplexus.info :: Numbers : Remainders

Remainders (Posted on 2006-04-15)

A={the set of all positive integers leaving a remainder of 4 when divided by 45}
B={the set of all positive integers leaving a remainder of 45 when divided by 454}
C={the set of all positive integers leaving a remainder of 454 when divided by 4545}
D={the set of all positive integers leaving a remainder of 4545 when divided by 45454}

Find the smallest number in the intersection of
1)Sets A and B;
2)Sets A and B and C;
3)Sets A and B and C and D.

Submitted by Jer

Rating: 4.0000 (2 votes)

Solution: (Hide)

499 = 11*45 + 4
499 = 1*454 + 45
41359 = 919*45 + 4
41359 = 91*454 + 45
41359 = 9*4545 + 454
35641667749 = 792037061*45 + 4
35641667749 = 78505876*454 + 45
35641667749 = 7841951*4545 + 454
35641667749 = 784126*45454 + 4545

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-08-04 09:04:16
re: computer solution	Richard	2006-04-16 16:02:32
computer solution	Charlie	2006-04-15 18:39:50
Part 1	Richard	2006-04-15 15:27:53

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