Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 916 · 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 6? (a) 6 (b) 5 (c) 7 (d) 10
2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 3 (b) 1 (c) 2 (d) 4
3. 3.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) 171 (b) 19 (c) 60 (d) 57
4. 4.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) 11 (b) 36 (c) 33 (d) 99
5. 5.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) 468 (d) 477
6. 6.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) 72 (c) 24 (d) 27
7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 4 (b) 3 (c) 6 (d) 5
8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 19 (d) 20
9. 9.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) 6 (b) 21 (c) 54 (d) 18
10. 10.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 242 (c) 246 (d) 256
11. 11.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) 90 (c) 30 (d) 33
12. 12.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 606 (c) 476 (d) 607
13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 3 (d) 5
14. 14.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 177 (b) 186 (c) 168 (d) 178
15. 15.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 313 (c) 312 (d) 303
16. 16.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
17. 17.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 192 (c) 183 (d) 193
18. 18.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 558 (d) 450
19. 19.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 9 (d) 18
21. 21.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
22. 22.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 3 (c) 2 (d) 4
23. 23.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) 48 (b) 135 (c) 45 (d) 15
24. 24.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 41 (d) 50
25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
26. 26.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) 81 (b) 9 (c) 30 (d) 27
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 9 (b) 21 (c) 19 (d) 20
28. 28.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 432 (d) 541
29. 29.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) 207 (b) 23 (c) 72 (d) 69
30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
31. 31.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 603 (c) 480 (d) 612
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 15 (b) 5 (c) 17 (d) 16
33. 33.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 185 (c) 176 (d) 186
34. 34.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 64 (c) 55 (d) 56
35. 35.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
36. 36.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 198 (c) 208 (d) 207
37. 37.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 18 (d) 1
38. 38.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 130 (c) 140 (d) 148
39. 39.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
40. 40.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) 66 (d) 22

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