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2016 小學數學競賽選拔賽初賽試題
第 一 試：計 算 題 (考試時間 1 小時)
◎
請將答案填入答案卷對應題號的空格內，不須計算過程。答案若為分數請化
為最簡分數。本題目卷正反面空白處可為作演算草稿紙。每題 5 分，共 100 分
1.
2 2 2 2 2 2 2 5 25 125
× × × × × × × × ×
=
？
(2 5) (2 2 25) (2 2 2 125) 2 10 100 1000 2
2000000
= × × × ×
× × × ×
× = ×
×
× =
2.
5 10 15
20
25
300
305 310
315
+ + +
+
+ +
+
+
+
=
⋯
？
(5 315) 63
10080
2
+
×
=
=
3.
10.08
20.16
30.32
40.64
51.28 8.07 12.15 16.31 20.63 25.27
+
+
+
+
−
−
−
−
−
=
？
(10
20
30
40
51 8 12 16
20
25)
(0.08 0.07
0.16
0.15
0.32
0.31 0.64
0.63 0.28 0.27)
70
0.05
70.05
=
+
+
+
+ − − − −
−
+
−
+
−
+
−
+
−
+
−
=
+
=
4.
167 399 167 399 167 399 167 399 167 399 167 399
×
+
×
+
×
+
×
+
×
+
×
=
？
167 399 6 167 6 399 1002 399
399798
=
×
× =
× ×
=
×
=
5.
164 164 3 164 5 164 7 164 9 164 11
+
× +
× +
× +
× +
× =
？
2
2
164 (1 3 5 7 9 11)
164 36
(100 64) (100 64)
100
64
10000 4096
5904
=
× + + + + +
=
×
=
+
×
−
=
−
=
−
=
6.
135789
357891 578913 789135 891357
913578
+
+
+
+
+
=
？
(1 3 5 7
8 9) 111111 33 111111 3666663
= + + + + + ×
= ×
=
7.
201.6 7.8 9 3 67.2 5 3.9
×
÷ × ÷
× ÷
=
？
67.2 3 7.8 9 3 67.2 5 3.9
67.2 67.2 3 3 9 7.8 3.9 5
2 5 10
=
× ×
÷ × ÷
× ÷
=
÷
× × ÷ ×
÷
× = × =
8.
2016
2015
2014
1010 1009 1008 1007
3 2 1
+
+
+ +
+
−
−
− − − − =
⋯
⋯
？
【參考解法
1
】
1008
(2016 1008)
(2015 1007)
(2014 1006)
(1010
2)
(1009 1)
1008 1008
1008 1008
1008 1008 1016064
=
−
+
−
+
−
+ +
− +
−
=
+
+ +
+
=
×
=
⋯
⋯
項
【參考解法
2
】
(2016
2015
2014
2 1)
2 (1008 1007
2 1)
(2016 1) 2016
(1008 1) 1008
2
2
2
1008 (2017 1009)
1008 1008 1016064
=
+
+
+ + + − ×
+
+ + +
+ ×
+ ×
=
− ×
=
×
−
=
×
=
⋯
⋯
9.
954 954 504 504
450 450
×
−
×
−
×
=
？
(954 504) (954 504)
450 450
1458 450 450 450
(1458 450) 450
1008 450
453600
=
+
×
−
−
×
=
×
−
×
=
−
×
=
×
=
10.
2016 7777
672 6666
×
+
×
=
？
2016 7777
672 3 2222
2016 7777
2016 2222
2016 (7777
2222)
2016 (10000 1)
20160000
2016
20157984
=
×
+
× ×
=
×
+
×
=
×
+
=
×
−
=
−
=
11.
1 3 6 10
4 12 24 40
7 21 42 70 10 30 60 100
2 5 7 11 8 20 28 44 14 35 49 77
20 50 70 110
× × × + × × ×
+ × × ×
+ × × ×
=
× × × + × × ×
+ × × ×
+
× × ×
？
1 3 6 10 (1 4 7 10)
1 3 6 10
18
2 5 7 11 (1 4 7 10)
2 5 7 11
77
× × × × + + +
× × ×
=
=
=
× × × × + + +
× × ×
12.
20.16 20.16
79.84 120.16
×
+
×
=
？
20.16 20.16
79.84 (20.16 100)
20.16 20.16
79.84 20.16
7984
20.16 (20.16
79.84)
7984
20.16 100
7984
2016
7984 10000
=
×
+
×
+
=
×
+
×
+
=
×
+
+
=
×
+
=
+
=
13.
28.8 199.99
2.88 1999.6
0.288 1.9993
×
−
×
−
×
=
？
288 (0.1 199.99 0.01 1999.6 0.001 1.9993)
288 (19.999 19.996 0.0019993)
288 0.0010007
0.2882016
=
×
×
−
×
−
×
=
×
−
−
=
×
=
14.
1
1
1
1
21
(5 2
4
)
0.9375
16
7
3
7
+ ×
− ÷ ÷ +
=
？
1
15
1
15
84
75
9
21
(5
12)
22 (
) 7
22
7 13
16
7
7
16
7
7
7
=
+ ×
−
÷ +
=
−
−
× =
− × =
15.
1169
214
89
1
8
1690
501
114
×
÷
=
？
1169
715
1001
1690
501
114
1169
715
114
7 167
5 11 13
2 3 19
19
19
1690
501 1001
2 5 13 13
3 167
7 11 13
13 13
169
=
×
÷
×
× ×
× ×
=
×
×
=
×
×
=
=
× × ×
×
× ×
×
16.
2015
2016
4033
2015
2016
2016
2017
2016 2017
×
+
×
−
=
×
？
1
1
2016 2017
2015 (1
)
2016 (1
) (
)
2016
2017
2016 2017
2015
2016
1
1
2015
2016
2016
2017
2017
2016
2015 2016 2
4029
+
=
× −
+
× −
−
×
=
−
+
−
−
−
=
+
− =
17.
91 929
9399 94999
959999
9699999
97999999
989999999
+
+
+
+
+
+
+
=
？
(90
2 1)
(900
30 1)
(9000
400 1)
(90000
5000 1)
(900000
60000 1)
(9000000
700000 1)
(90000000 8000000 1)
(900000000
90000000 1)
90
900 9000
90000 900000
9000000
90000000
900000000
2 30
400
5000
60000
=
+ − +
+
− +
+
− +
+
−
+
+
− +
+
− +
+
−
+
+
−
=
+
+
+
+
+
+
+
+ +
+
+
+
700000 80000000
90000000 8
999999990
98765432 8
1000000000 10
98765432 8
1098765432 18
1098765414
+
+
+
−
=
+
−
=
− +
−
=
−
=
18.
1
2
14
30
62
1 2
1 2 4
1 2 4 8
1 2 4 8 16
1 2 4 8 16 32
−
−
−
−
=
×
× ×
× × ×
× × × ×
× × × × ×
？
4
2
14
30
62
1 2 4
1 2 4
1 2 4 8
1 2 4 8 16
1 2 4 8 16 32
2
14
30
62
1 2 4
1 2 4 8
1 2 4 8 16
1 2 4 8 16 32
16
14
30
62
1 2 4 8
1 2 4 8
1 2 4 8 16
1 2 4 8 16 32
2
30
62
1 2 4 8
1 2 4 8 16
1 2 4 8 16 32
32
1 2 4 8 16
=
−
−
−
−
× ×
× ×
× × ×
× × × ×
× × × × ×
=
−
−
−
× ×
× × ×
× × × ×
× × × × ×
=
−
−
−
× × ×
× × ×
× × × ×
× × × × ×
=
−
−
× × ×
× × × ×
× × × × ×
=
−
× × × ×
14
14
30
62
1 2 4 8 16
1 2 4 8 16 32
2
62
1 2 4 8 16
1 2 4 8 16 32
64
62
1 2 4 8 16 32
1 2 4 8 16 32
2
1 2 4 8 16 32
1
1
2
2
16384
−
−
× × × ×
× × × × ×
=
−
× × × ×
× × × × ×
=
−
× × × × ×
× × × × ×
=
× × × × ×
=
=
=
19.
485359
323
81018
(20
) 10
999999
999
999999
−
÷
=
？
20485339
323323
10081008
(
)
999999
999999
999999
20162016
999999
999999
10081008
20162016
10081008
2
=
−
÷
=
×
=
=
20.
33 27
22 18 9
4
(33 27
22 18 9
4)
125
(33 27
22 18 9
4)
9
(33 27
22 18 9
4)
75
(33 27
22 18 9
4)
30
(33 27
22 18 9
4)
48
250
×
−
× + −
=
×
−
× + −
+
×
−
× + −
−
×
−
× + −
+
×
−
× + −
−
×
−
× + −
+
？
2
2
2
2
2
2
33 27
22 18 9
4
(30
3) (30 3)
9
(20
2) (20
2)
4
30
3
9
20
2
4
30
20
500
×
−
× + − =
+ ×
− + −
+ ×
− −
=
− + −
+ −
=
−
=
因
故知原式等價於
500
500
500
500
500
500
125
125
125
500
500
500
9
9
9
500
500
500
75
75
75
500
500
500
30
30
30
500
48
2
50
48
250
500
500
500
500
125
125
500
500
9
9
500
500
75
75
30 10
20
500
500
500
500
500
500
125
125
125
500
500
9
9
75
25
100
=
=
+
+
+
−
−
−
+
+
+
−
−
−
+
+
=
=
+
+
−
−
+
+
−
=
=
=
+
+
+
−
−
+
9 5
500
500
500
2
500
125 125
250
125
4
−
=
=
=
=
+
+