Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 306 · 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 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) 48 (c) 135 (d) 45
2. 2.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
3. 3.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 625 (c) 615 (d) 624
4. 4.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
5. 5.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) 72 (b) 216 (c) 75 (d) 24
6. 6.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
7. 7.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) 27 (b) 8 (c) 24 (d) 72
8. 8.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 19 (b) 18 (c) 7 (d) 17
10. 10.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 498 (c) 630 (d) 640
11. 11.The numbers 16 to 24 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) 180 (c) 20 (d) 60
12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
13. 13.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 14 (d) 13
15. 15.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
16. 16.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 320 (b) 372 (c) 363 (d) 373
17. 17.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) 57 (b) 19 (c) 171 (d) 60
18. 18.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 474 (c) 465 (d) 475
19. 19.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 339 (c) 348 (d) 349
20. 20.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 129 (c) 130 (d) 138
21. 21.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 51 (b) 52 (c) 42 (d) 60
22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 2 (b) 4 (c) 3 (d) 5
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) 207 (b) 72 (c) 69 (d) 23
24. 24.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 13 (b) 9 (c) 12 (d) 10
26. 26.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) 162 (b) 57 (c) 18 (d) 54
27. 27.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 9 (d) 8
28. 28.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 397 (c) 336 (d) 387
29. 29.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) 15 (c) 18 (d) 45
30. 30.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) 126 (c) 42 (d) 45
31. 31.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 158 (c) 167 (d) 176
32. 32.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) 153 (b) 54 (c) 51 (d) 17
33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 21 (b) 20 (c) 9 (d) 19
34. 34.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) 480 (c) 603 (d) 612
35. 35.A book has 154 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 308 (b) 345 (c) 355 (d) 354
36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 14 (b) 15 (c) 16 (d) 5
37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 5 (c) 6 (d) 4
38. 38.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 280 (c) 258 (d) 279
39. 39.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 166 (c) 148 (d) 158
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 16 (b) 9 (c) 15 (d) 13

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