Latest Maths Olympiad Aptitude Question SOLUTION: Q. Begin with any two-digit positive integers and multiply the two digit together. If the result product in a two-digit number, then repeat the process. When this process is repeat

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Q. Begin with any two-digit positive integers and multiply the two digit together. If the result product in a two-digit number, then repeat the process. When this process is repeated, all two digit numbers will eventually become a single digit number. Once a product results in a single digit, the process stops.

a) Beginning with number 68, determine the no. of steps required for the process to stop
b)Determine all two digit numbers for which the process stops at 8 after 2 steps.
c) Determine all two digit no. for which the process stops at 4
d) Determine a two digit number for which the process stops after 4 steps

Asked In Maths Olympiad Sanjana Patnaik (12 years ago)

Solved Dr.Dipin Singh Read Solution (2)

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Dr.Dipin Singh  (12 years ago)

a)
Beginning with number 68,
68 ..6*8= 48...4*8=32....3*2= 6
the no. of steps required for the process to stop = 3 steps
b)to determine all two digit numbers for which the process stops at 8 after 2 steps.

8.. previous numbers can be 42,24,18,81 ... previous numbers can be
76,67
38,83,46,64
36,63,29,92,
99
so total 11 numbers

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Rakesh  (11 years ago)

a=3
1st step=6*8=48; then 4*8=32; then 3*2=6
b= it wanted final number to be 8; 8=2*4;4*2;1*8;8*1 so possible number=42,24,18,81 and for getting these
42=(6.7;7.6)
24=(6.4;4.6;8.3;3.8)
18=(2.9;9.2;6.3;3.6)
81=(9.9)

c= for 4 to be the final digit possile ways are (2*2;1*4;4*1)

so possble numbers are 22,14,41

d.

This is a beautiful question initially i tried picking random big numbers liek 78,98,86 and all and tried but it was taking time you see.. its difficult to find this answer via trial and error method, so go from single digit like...
6=32=48=68.. u can inter change these number. so when i did that for 9=18=36=49=77 i found it.. answer to this is 77

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