Math worksheet focusing on modular arithmetic, designed as a Sudoku puzzle with 26 modulo-based problems to solve.

Explanation:
We are given a list of modular arithmetic problems. For each expression like “a mod b”, we need to find the remainder when a is divided by b.

Recall:
- The result of `a mod b` is the remainder after dividing `a` by `b`.
- It must be a non-negative integer less than `b`.
- Example: `17 mod 9 = 8`, because 9 × 1 = 9, and 17 − 9 = 8.

Let’s go one by one:

a. 17 mod 9
17 ÷ 9 = 1 remainder 8 → 8

b. 11 mod 6
11 ÷ 6 = 1 remainder 5 → 5

c. 26 mod 4
26 ÷ 4 = 6 × 4 = 24, remainder 2 → 2

d. 24 mod 10
24 ÷ 10 = 2 × 10 = 20, remainder 4 → 4

e. 18 mod 11
18 − 11 = 7 → 7

f. 18 mod 8
18 ÷ 8 = 2 × 8 = 16, remainder 2 → 2

g. 3 mod 9
3 < 9, so remainder is just 3 → 3

h. 30 mod 12
12 × 2 = 24, 30 − 24 = 6 → 6

i. 20 mod 14
14 × 1 = 14, 20 − 14 = 6 → 6

j. 99 mod 10
Any number mod 10 is its last digit → 99 ends in 9 → 9

k. 32 mod 7
7 × 4 = 28, 32 − 28 = 4 → 4

l. 9 mod 12
9 < 12 → remainder is 9 → 9

m. 33 mod 6
6 × 5 = 30, 33 − 30 = 3 → 3

n. 46 mod 10
Last digit of 46 is 6 → 6

o. 50 mod 9
9 × 5 = 45, 50 − 45 = 5 → 5

p. 32 mod 13
13 × 2 = 26, 32 − 26 = 6 → 6

q. 33 mod 8
8 × 4 = 32, 33 − 32 = 1 → 1

r. 26 mod 11
11 × 2 = 22, 26 − 22 = 4 → 4

s. 19 mod 13
13 × 1 = 13, 19 − 13 = 6 → 6

t. 13 mod 8
8 × 1 = 8, 13 − 8 = 5 → 5

u. 21 mod 6
6 × 3 = 18, 21 − 18 = 3 → 3

v. 17 mod 7
7 × 2 = 14, 17 − 14 = 3 → 3

w. 20 mod 13
13 × 1 = 13, 20 − 13 = 7 → 7

x. 7 mod 8
7 < 8 → remainder is 7 → 7

y. 21 mod 12
12 × 1 = 12, 21 − 12 = 9 → 9

z. 21 mod 12 — same as y? Wait! Look again:
The list shows:
- y. 21mod12
- z. 21mod12

That seems like a duplicate. But since both are “21 mod 12”, answer is still 9.

Let me double-check all calculations quickly:

a. 17−9=8 ✔
b. 11−6=5 ✔
c. 26−24=2 ✔
d. 24−20=4 ✔
e. 18−11=7 ✔
f. 18−16=2 ✔
g. 3 ✔
h. 30−24=6 ✔
i. 20−14=6 ✔
j. 99→9 ✔
k. 32−28=4 ✔
l. 9 ✔
m. 33−30=3 ✔
n. 46→6 ✔
o. 50−45=5 ✔
p. 32−26=6 ✔
q. 33−32=1 ✔
r. 26−22=4 ✔
s. 19−13=6 ✔
t. 13−8=5 ✔
u. 21−18=3 ✔
v. 17−14=3 ✔
w. 20−13=7 ✔
x. 7 ✔
y. 21−12=9 ✔
z. same as y → 9 ✔

All correct.

Final Answer:
a. 8
b. 5
c. 2
d. 4
e. 7
f. 2
g. 3
h. 6
i. 6
j. 9
k. 4
l. 9
m. 3
n. 6
o. 5
p. 6
q. 1
r. 4
s. 6
t. 5
u. 3
v. 3
w. 7
x. 7
y. 9
z. 9