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11 DPS Chains onible slenshT SI 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 3 x 5 x 7 = 105 2 x 5 x 2 = 20 2 x 3 x 2 = 12 2x2x0=0 381 24 357 357 105 = 252 20 232 12 = 220 2200 220. 252 232 - - - So 220 is the last number in this DPS chain. The DPS chain can be written as 381357252232220. 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.

11 DPS Chains onible slenshT SI 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 3 x 5 x 7 = 105 2 x 5 x 2 = 20 2 x 3 x 2 = 12 2x2x0=0 381 24 357 357 105 = 252 20 232 12 = 220 2200 220. 252 232 - - - So 220 is the last number in this DPS chain. The DPS chain can be written as 381357252232220. 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.

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 11 DPS Chains eniblo elenshT SI 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 3x8x1 = 24 3x5x7= 105 2× 5 × 2 = 20 2 × 3 × 2 = 12 2×2×0=0 381 24 357 357 - 105 = 252 252 20 = 232 232 12 = 220 220 - 0 = 220. - - - 3 So 220 is the last number in this DPS chain. The DPS chain can be 357252232 220. It has 5 numbers so we say written as 381 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.
Transcribed Image Text:Intermediate Problems 11 DPS Chains eniblo elenshT SI 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 3x8x1 = 24 3x5x7= 105 2× 5 × 2 = 20 2 × 3 × 2 = 12 2×2×0=0 381 24 357 357 - 105 = 252 252 20 = 232 232 12 = 220 220 - 0 = 220. - - - 3 So 220 is the last number in this DPS chain. The DPS chain can be 357252232 220. It has 5 numbers so we say written as 381 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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