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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Tom's Number

Age 7 to 11
Challenge Level

"Guess my number," said Tom, "I'll only answer yes or no."

yes or no?

"OK. Is it less than $1000$?" "No."
"Is it less than $2000$?" "Yes."
"Is it even?" "No."
"So it's an odd number between $1000$ and $2000$?"
"Yes, but you knew that already. It's a wasted question!"
"Is it divisible by $3$?" "No."
"Is it divisible by $5$?" "No."
"Is it divisible by $7$?" "Yes."
"If I divide it by $7$ do I get a number that is less than $100$?" "No."
"Do I get a number that is less than $200$?" "Yes."
"Ah! $100 \times 7$ = $700$ and $200 \times 7 = 1400$. So your number is less than $1400$?"
"Yes, but that's another wasted question."
"Ha! $14$ squared is $196$.
So your number is $7$ times the product of two prime numbers less than $14$?"
"I am sure I know your number and this question is just checking.
Is your number palendromic? Does it read the same in both directions?"

What was Tom's number?