Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 272 · 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) 66 (b) 189 (c) 21 (d) 63
2. 2.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) 72 (c) 24 (d) 8
3. 3.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 216 (c) 225 (d) 222
4. 4.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
6. 6.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) 54 (b) 51 (c) 153 (d) 17
7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 2 (d) 3
8. 8.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
9. 9.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 156 (c) 138 (d) 147
10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 8 (b) 6 (c) 5 (d) 7
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) 33 (b) 10 (c) 90 (d) 30
12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 4 (b) 3 (c) 6 (d) 7
13. 13.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) 57 (c) 19 (d) 60
14. 14.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
15. 15.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 439 (d) 438
16. 16.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) 72 (b) 23 (c) 69 (d) 207
17. 17.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) 18 (c) 21 (d) 6
18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 5 (d) 3
19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 9 (b) 4 (c) 6 (d) 8
20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
21. 21.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) 18 (b) 57 (c) 54 (d) 162
22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 3 (c) 14 (d) 13
23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 18 (d) 17
24. 24.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) 45 (c) 126 (d) 14
25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 18 (c) 7 (d) 17
26. 26.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 4 (d) 6
28. 28.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 445 (c) 368 (d) 444
29. 29.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 553 (d) 552
30. 30.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 279 (c) 289 (d) 288
31. 31.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 5 (d) 15
33. 33.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 3 (b) 5 (c) 4 (d) 6
35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
36. 36.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) 198 (c) 66 (d) 22
37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 7 (b) 9 (c) 6 (d) 8
38. 38.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 101 (c) 102 (d) 110
39. 39.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 174 (d) 184
40. 40.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) 180 (b) 60 (c) 63 (d) 20

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