11 DPS Chains A Digit Product Submetion (DPS) cham starts with any number with two or more digits The protoct of its digits i subtracted from the number to form the sert number in the chain. This is repeated until the answer does not change. For example, starting with the 3-digit munner 381 gives 381-24 357 357-105=252 232-20-232 232-12-220 220-0-220. 3x8x1=24 3x5×7=105 2x5x2=20 2x3x2=12 2x2x0=0 So 220 in the last number in the 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 & that starts with a 2-digit number. b Find a DPS chain of length 3 that ends at 40. e Explain why & DPS chain that starts with a 2-digit nunner containe only 2-digit numbera d Find a DPS chain of length 3 that ends as 307
okay so the last time i tried to ask this it was supposedly a violation of the tos, my guess is as the question was already there and i reused the image as all i had on me at the time was a crap built in webcam but heres the photo i took so it coincides with the tos rules.
Transcription: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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