Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 613 · 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.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 340 (c) 403 (d) 402
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 20 (d) 19
3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 7 (b) 6 (c) 8 (d) 9
4. 4.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 16 (d) 15
6. 6.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 15 (d) 4
8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 20 (d) 21
9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 16 (b) 14 (c) 5 (d) 15
10. 10.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 102 (c) 93 (d) 94
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 18 (b) 16 (c) 17 (d) 6
12. 12.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) 9 (b) 30 (c) 81 (d) 27
13. 13.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
14. 14.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) 198 (b) 69 (c) 22 (d) 66
15. 15.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 17 (b) 16 (c) 5 (d) 15
17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 17 (d) 7
18. 18.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 18 (d) 17
20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 16 (b) 5 (c) 17 (d) 15
21. 21.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) 23 (c) 72 (d) 207
22. 22.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 350 (c) 417 (d) 418
23. 23.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) 39 (c) 117 (d) 13
24. 24.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 190 (c) 198 (d) 189
25. 25.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 478 (c) 477 (d) 468
26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 13 (b) 11 (c) 14 (d) 8
27. 27.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 348 (c) 358 (d) 357
28. 28.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) 18 (c) 162 (d) 57
29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 9 (d) 20
30. 30.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
31. 31.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) 8 (b) 27 (c) 72 (d) 24
32. 32.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) 63 (b) 24 (c) 7 (d) 21
33. 33.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 15 (b) 16 (c) 14 (d) 5
35. 35.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) 45 (b) 5 (c) 15 (d) 18
36. 36.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 72 (c) 82 (d) 90
37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 9 (c) 8 (d) 10
38. 38.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 372 (c) 382 (d) 381
39. 39.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 90 (d) 30
40. 40.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 328 (c) 385 (d) 375

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