Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 665 · 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 7? (a) 8 (b) 6 (c) 10 (d) 7
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 17 (d) 19
3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 3 (b) 1 (c) 4 (d) 2
4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 4 (d) 6
5. 5.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) 27 (d) 24
6. 6.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
7. 7.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 411 (c) 420 (d) 421
8. 8.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 338 (c) 390 (d) 399
9. 9.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 265 (b) 255 (c) 264 (d) 248
10. 10.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
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.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 450 (c) 451 (d) 372
13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 4 (b) 12 (c) 14 (d) 13
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 14 (d) 13
15. 15.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
16. 16.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
17. 17.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 348 (c) 358 (d) 310
18. 18.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 141 (c) 150 (d) 142
19. 19.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
20. 20.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
21. 21.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 384 (c) 468 (d) 459
22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 16 (b) 17 (c) 15 (d) 5
23. 23.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
25. 25.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) 18 (c) 15 (d) 45
26. 26.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 1
28. 28.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) 51 (b) 16 (c) 144 (d) 48
29. 29.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
30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 2 (d) 3
31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 18 (d) 17
32. 32.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 69 (c) 70 (d) 60
33. 33.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) 54 (c) 18 (d) 21
34. 34.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 159 (c) 168 (d) 160
35. 35.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
36. 36.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) 21 (c) 63 (d) 189
37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
38. 38.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) 336 (c) 397 (d) 387
39. 39.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) 207 (c) 69 (d) 23
40. 40.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) 24 (d) 75

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