p7. An ant starts at the point (0,0). It travels along the integer lattice, at each lattice point choosing the positive x or y direction with equal probability. If the ant reaches (20,23), what is the probability it did not pass through (20,20)?
p8. Let a0=2023 and an be the sum of all divisors of an−1 for all n≥1. Compute the sum of the prime numbers that divide a3.
p9. Five circles of radius one are stored in a box of base length five as in the following diagram. How far above the base of the box are the upper circles touching the sides of the box?
https://cdn.artofproblemsolving.com/attachments/7/c/c20b5fa21fbd8ce791358fd888ed78fcdb7646.png
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