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 Four Digit and Two Digit Treat (Posted on 2015-12-13)
The respective two digit numbers 20 and 16 are formed by considering the first two digits and the last two digits of 2016 in order. Also, 2016/(20+16)= 56, so that, 2016 is evenly divisible by the sum of the two 2-digit numbers considering its first two digits and the last two digits.

(i) Determine five numbers following 2016 that possess this property.

(ii) Determine five numbers preceding 2016 that possess this property.

*** No leading zero is permissible for any of the numbers.

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 1 of 1
Checked from 1500 to 2599. The results:

(If, by leading zeros, one means to disallow, such numbers as 2002 on the basis of 02, then in the bolded section below, substitute numbers from the non-bolded area prior to 1980.)

1500
1512
1518
1530
1540
1584
1600
1602
1606
1608
1617
1620
1628
1632
1650
1656
1672
1683
1700
1716
1734
1782
1800
1804
1809
1815
1836
1848
1863
1881
1900
1914
1938

1980
2000
2002
2010
2013

2016

2024
2025
2035
2040
2046

2070
2079
2090
2100
2106
2112
2142
2156
2178
2200
2211
2244
2277
2299
2300
2310
2346
2376
2400
2403
2409
2412
2420
2430
2442
2448
2464
2475
2484
2500
2508
2520
2530
2550
2574

DefDbl A-Z
Dim crlf\$

Private Sub Form_Load()
Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For a = 15 To 25
For b = 0 To 99
n = 100 * a + b
If n Mod (a + b) = 0 Then
Text1.Text = Text1.Text & n & crlf
End If
Next
Next

Text1.Text = Text1.Text & crlf & " done"

End Sub

Edited on December 13, 2015, 6:27 pm
 Posted by Charlie on 2015-12-13 18:21:48

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