Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 492 · 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.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
2. 2.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 17 (d) 6
4. 4.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) 51 (b) 54 (c) 153 (d) 17
5. 5.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 39 (d) 12
6. 6.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 384 (c) 375 (d) 385
7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 15 (c) 4 (d) 14
8. 8.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
9. 9.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
10. 10.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 324 (c) 334 (d) 333
11. 11.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 9 (c) 27 (d) 81
12. 12.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
13. 13.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
14. 14.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
15. 15.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 117 (c) 13 (d) 39
16. 16.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 223 (c) 222 (d) 220
17. 17.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) 45 (b) 48 (c) 135 (d) 15
18. 18.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
19. 19.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) 42 (b) 14 (c) 126 (d) 45
20. 20.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 170 (c) 152 (d) 161
21. 21.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 200 (c) 183 (d) 192
22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 1 (c) 4 (d) 2
23. 23.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 582 (c) 573 (d) 460
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 18 (d) 19
25. 25.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 8 (d) 7
26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 5 (b) 2 (c) 3 (d) 4
27. 27.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 96 (c) 106 (d) 114
28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 17 (d) 18
29. 29.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 216 (c) 207 (d) 324
30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 3 (b) 1 (c) 4 (d) 2
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
32. 32.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 68 (c) 86 (d) 77
33. 33.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 216 (c) 75 (d) 72
34. 34.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 446 (c) 561 (d) 552
35. 35.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
37. 37.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 444 (c) 435 (d) 368
38. 38.The numbers 3 to 11 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) 7 (c) 24 (d) 63
39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 6 (d) 5
40. 40.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) 54 (b) 6 (c) 18 (d) 21

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