# Varsity Math, Week 136

## ________________

The coach likes logic problems where one of the participants is blindfolded but, nevertheless, can still prevail over the other participants.

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### Sevens and Elevens

Participants are told there are nine slips of paper. Five of those slips have the number 7 on them, while the other four have 11 on them. Alice, Bob, Carl, Dave and Edward have one of the slips on each of their hats. The other four slips remain hidden. Edward is blindfolded, but the others can see all numbers except their own. They are asked in turn to identify their number. All participants hear the responses of any that go before them.

Alice: “I don’t know my number.”
Bob: “I don’t know my number.”
Carl: “I don’t know mine.”
Dave: “I don’t know mine.”
Edward: “I know my number.”

What number is on Edward?

### Three-Digit Squares

Each of team members Alice, Bob, and Carl wears a hat with a single digit from 0 to 9 on it. In an unknown order, they are the digits of a square having three digits. Alice and Carl can see the digits on the other two hats but not their own. Bob is blindfolded. After being asked to deduce their digits, there is quite a long silence after which Bob announces, “I know my digit.”

What digit is on Bob and what are the possibilities for digits on Alice and Carl?

## Solutions to week 135

The solution to Batting Order is 385274961 and 941638527. In Swimming Workout, Randall swam 2 miles in total at a speed of 0.8 miles an hour in the lake.