# INTERNATIONAL CONTEST OF LOGICAL SEQUENCES 2002 - 2003

## Solutions

Albert Frank

The winner is Edward Vanhove (member of Glia), with 18/20
Second: Rich Rector, 17/20
Third: Eric Wyckmans, 16/20

1) 2, 6, 15, ?, 55, ?, 119
28, 78 : n times n-th prime
2) 4, ?, 5, 2, 6, 10, 3, 7, 6
2 : digits of Pi + 1
3) 1, 3, 9, 9, 9, 9, 18, 18, 18, 27, 27, ?, ?
27, 18 : sum of the digits of 3^n (n = 0,1,2,…)
4) 0, 0, 2, 0, 2, 4, 2, 0, ?, ?
8, 4 : 2^n modulo n (n = 1,2,3,…)
5) 6, 3, 20, 7, ?, 117, ?, 114
55, 34 : digits of Pi x prime numbers
6) 6, 7, 2, 1, 5, 9, ?, ?, ?
8, 3, 4 : third line of the magic square 3x3 with 672 on line 1
7) ?, -1, -1, -1, 0, 2, 6, 13, 25, ?
0, 45 : n-th Fibonacci number - n
8) 2614534, 4?45??
464531 : read : 2nd term is 6, 6th term is 1, 1st term is 4, ...
9) 1, 2, 3, 5, 8, 10, ?, 16, 23
13 : sum of the digits of 1, 11, 21, 1211, …
10) 1010, 202, 132, 130, 122, 114, 106, ?, 90
88 : 10 times n in the base (n+1)
11) 4, 9, 7, 13, ?, 16, 19, ?, 16, 13
4, 10 : sum of digits of (prime numbers^2)
12) Why are there two * in the following finite sequence ?
1, 5, 9, 6, 3, *, 2, 4, *, 7, 8, 9
symbolic writing of the " 9 points " problem.
13) 5, 6, 7, 8, 8, 8, 8, ?, ?
8, 9 : first non zero digit of ½, 2/3, ¾, …
14) 4, 6, 10, ?, 3, 7, 15, 19, 11, ?
14, 29 : sum + product of digits of the prime numbers
15) 6, 14, 6, 5, 40, 90, 104, ?
48 : question 6) x question 9)
16) -1, -1, 1, 17, 109, 707, ?
5023 : n ! - n-th prime number
17) 1, 2, 3, 6, ?, 6, 3, 6, 1
1 : Pi written following e (1 = 2nd digit of Pi, 2 = 7th digit of Pi, 3 = 1st digit of Pi, 6 = 8th digit of Pi, ...
18) 0, 1, 2, 3, 1, 1, ?, 3, ?, 9
3, 5 : nth prime number modulo n
19) 11, 23, 44, 56, 48, 67, ?
88 : 1 of the short ways (7 moves) for a knigth to go, on a chessboard, from one corner to the opposite corner
20) 1, 2, 2, 1, 2, 4, 2, 2, 1, 2, ?, 2, 2, 1, 2, 2, 2, ?, 2, 1
2, 1 : Throw of 2 dices. Probability x 36, by increasing order, of the values of (sum + product)