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.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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