Answered: So 220 is the last number in this DPS… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 26EQ

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Intermediate Problems
3.
11 DPS Chains
A Digit Product Subtraction (DPS) chain starts with any number with
two or more digits. The product of its digits is subtracted from the
number to form the next number in the chain. This is repeated until the
answer does not change.
For example, starting with the 3-digit number 381 gives
3 x 8 x 1=24
381 24 357
3 x 5 x 7= 105
357 – 105 = 252
2 x 5 x 2 = 20
252 20 232
2 x 3 x 2 = 12
232 12 220
%3D
2 x 2 x 0 = 0
220 0 220.
So 220 is the last number in this DPS chain. The DPS chain can be
written as 381 357→252 232 220. It has 5 numbers so we say
the chain has length 5.
a Find a DPS chain of length 5 that starts with a 2-digit number.
b Find a DPS chain of length 3 that ends at 40.
c Explain why a DPS chain that starts with a 2-digit number contains
only 2-digit numbers.
d Find a DPS chain of length 3 that ends at 307.

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