Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 129 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 66 (c) 63 (d) 189
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 14 (b) 15 (c) 16 (d) 4
3. 3.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 417 (c) 408 (d) 418
4. 4.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 45 (c) 42 (d) 126
5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 14 (d) 15
6. 6.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 411 (c) 420 (d) 352
7. 7.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
8. 8.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 18 (d) 19
10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 7 (d) 18
11. 11.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 27 (c) 24 (d) 8
12. 12.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 171 (c) 57 (d) 19
13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 4 (d) 3
14. 14.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 153 (d) 54
15. 15.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 66 (d) 198
16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 16 (b) 5 (c) 14 (d) 15
17. 17.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 144 (b) 16 (c) 51 (d) 48
18. 18.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
19. 19.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
20. 20.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 433 (d) 432
21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 7 (b) 6 (c) 4 (d) 5
22. 22.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
23. 23.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 207 (c) 23 (d) 72
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 15 (d) 17
25. 25.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 162 (c) 18 (d) 57
26. 26.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
27. 27.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 48 (c) 56 (d) 47
28. 28.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
29. 29.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 384 (c) 393 (d) 394
30. 30.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 15 (d) 45
31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 5 (d) 4
32. 32.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 6 (d) 21
33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 15 (b) 4 (c) 14 (d) 16
34. 34.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 45 (c) 135 (d) 48
35. 35.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 235 (b) 228 (c) 225 (d) 234
36. 36.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
37. 37.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 36 (c) 11 (d) 99
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 3 (b) 4 (c) 5 (d) 2
39. 39.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 337 (b) 327 (c) 336 (d) 296
40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 18 (b) 17 (c) 8 (d) 19

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